MSc Statistical Rob correction -Jan29
Housekeeping
Preamble
By Katherine Duchesneau
We are working with the roots Lesion and Mycorrhiza dataset for now.
R details
This section contains all the necessary details about the R version and package version used to run this Notebook.
- File creation date: 2018-02-05
- R version 3.4.1 (2017-06-30)
tidyversepackage version: 1.2.1lme4package version 1.1.13MASSpackage version 7.3.47MuMInpackage version 1.15.6emmeanspackage version 0.9.1bootpackage version 1.3.20brmspackage version 2.0.1loopackage version 1.1.0fitdistrpluspackage version 1.0.9mefapackage version 3.2.7library(devtools)andinstall_github("vqv/ggbiplot")package version 0.55- also requires rtools
Load Packages and Functions
library(tidyverse)
library(lme4)
library(MASS)
library(MuMIn)
library(emmeans)
library(boot)
library(brms)
library(loo)
library(fitdistrplus)
library(mefa)
library(ggbiplot)
library(pvclust)
library(vegan)
library(ggbiplot)Load a custome theme for clean, readable graphs:
Overdispersion function, tests for overdispersion in GLMM:
Introducing the Data
Load/ Modify data: Co-occurence
## [1] 99.55752## [1] 100## indiv2 None.Path None.Myc Herbivory
## 10IAH1 : 100 Length:22500 Length:22500 Min. :0.00000
## 10IAH2 : 100 Class :character Class :character 1st Qu.:0.00000
## 10ISC1 : 100 Mode :character Mode :character Median :0.00000
## 10ISC2 : 100 Mean :0.03658
## 10ISC3 : 100 3rd Qu.:0.00000
## 10OAH1 : 100 Max. :1.00000
## (Other):21900
## None.Herb Lesion Mycorrhiza
## Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:1.0000 1st Qu.:0.000 1st Qu.:0.0000
## Median :1.0000 Median :1.000 Median :1.0000
## Mean :0.9631 Mean :0.622 Mean :0.5732
## 3rd Qu.:1.0000 3rd Qu.:1.000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.000 Max. :1.0000
## ## indiv2 None.Path None.Myc Herbivory
## Length:22500 Min. :0.000 Min. :0.0000 Min. :0.00000
## Class :character 1st Qu.:0.000 1st Qu.:0.0000 1st Qu.:0.00000
## Mode :character Median :0.000 Median :0.0000 Median :0.00000
## Mean :0.378 Mean :0.4268 Mean :0.03658
## 3rd Qu.:1.000 3rd Qu.:1.0000 3rd Qu.:0.00000
## Max. :1.000 Max. :1.0000 Max. :1.00000
##
## None.Herb Lesion Mycorrhiza pop
## Min. :0.0000 Min. :0.000 Min. :0.0000 5 :2900
## 1st Qu.:1.0000 1st Qu.:0.000 1st Qu.:0.0000 7 :2600
## Median :1.0000 Median :1.000 Median :1.0000 8 :2600
## Mean :0.9634 Mean :0.622 Mean :0.5732 3 :2200
## 3rd Qu.:1.0000 3rd Qu.:1.000 3rd Qu.:1.0000 4 :2200
## Max. :1.0000 Max. :1.000 Max. :1.0000 1 :2000
## (Other):8000
## location species
## I:10600 AH:3100
## O:11900 CL:3900
## GA:4900
## GR:1300
## MR:3100
## SC:6200
## ## indiv2 None.Path None.Myc Herbivory None.Herb Lesion
## Length:22500 0:13995 0:12897 0:21677 0: 823 0: 8505
## Class :character 1: 8505 1: 9603 1: 823 1:21677 1:13995
## Mode :character
##
##
##
##
## Mycorrhiza pop location species
## 0: 9603 5 :2900 I:10600 AH:3100
## 1:12897 7 :2600 O:11900 CL:3900
## 8 :2600 GA:4900
## 3 :2200 GR:1300
## 4 :2200 MR:3100
## 1 :2000 SC:6200
## (Other):8000## [1] 225Load/ Modify data: Totals
## [1] 226## [1] 226## indiv Decay Pathogen Hyphae
## 10IAH1 : 1 Min. : 0.000 Min. : 0.000 Min. : 2.00
## 10IAH2 : 1 1st Qu.: 1.000 1st Qu.: 2.000 1st Qu.:34.00
## 10ISC1 : 1 Median : 4.000 Median : 4.000 Median :48.00
## 10ISC2 : 1 Mean : 7.894 Mean : 7.168 Mean :47.23
## 10ISC3 : 1 3rd Qu.: 9.000 3rd Qu.:10.000 3rd Qu.:63.00
## 10OAH1 : 1 Max. :60.000 Max. :86.000 Max. :96.00
## (Other):220
## None.Path Arbuscules Vesicles M_Hyphae
## Min. : 0.00 Min. : 0.000 Min. : 0.000 Min. : 0.00
## 1st Qu.:20.00 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.:30.25
## Median :33.00 Median : 0.000 Median : 6.000 Median :46.00
## Mean :37.71 Mean : 2.363 Mean : 9.956 Mean :45.16
## 3rd Qu.:53.75 3rd Qu.: 3.000 3rd Qu.:14.000 3rd Qu.:61.00
## Max. :97.00 Max. :21.000 Max. :73.000 Max. :94.00
##
## None.Myc Herbivory None.Herb pop location
## Min. : 0.00 Min. : 0.000 Min. : 62.00 5 :29 I:106
## 1st Qu.: 18.00 1st Qu.: 0.000 1st Qu.: 96.00 8 :27 O:120
## Median : 38.50 Median : 1.000 Median : 99.00 7 :26
## Mean : 42.52 Mean : 3.624 Mean : 96.38 3 :22
## 3rd Qu.: 66.00 3rd Qu.: 4.000 3rd Qu.:100.00 4 :22
## Max. :100.00 Max. :38.000 Max. :100.00 1 :20
## (Other):80
## species
## AH:31
## CL:39
## GA:50
## GR:13
## MR:31
## SC:62
## Field survey data
FloristicSurvey <-read.csv("CSV/May_2017_FloristicSurvey_summer2016.csv", sep="\t")
PlantLength <- read.csv("CSV/May_2017_PlantLength_summer2016.csv", sep="\t")
Soil_characteristics <- read.csv("CSV/Soil_characteristics.txt", sep="\t")
#Restructuring
head(PlantLength)str(PlantLength)## 'data.frame': 231 obs. of 4 variables:
## $ Pop : int 14 14 14 14 14 14 14 14 14 14 ...
## $ Location : Factor w/ 2 levels "in","out": 2 2 2 2 2 1 1 1 1 1 ...
## $ Species : Factor w/ 7 levels "Acer_saccharum",..: 1 4 3 5 7 1 4 3 5 7 ...
## $ Length_plant: num 14 87 20 12 67 11 65 51 20 100 ...colnames(PlantLength)[1] <- "Population"
PlantLength$Population<-as.factor(PlantLength$Population)
PlantLength$Location<-as.factor(PlantLength$Location)Root size
Root_size <-read.csv("CSV/Root_size.csv")Variable descriptions
The variables are:
Co-occurence:
indiv2: The unique code given to a sample. In this dataset the unique sample code repeats 100 times for each cross where an observation was taken on the root sample.
None.Path: A binary representation of whether a sign of pathogen activity was recorded (0) or not (1).
Lesion: The counterpart to the previous variable (None.Path). A binary representation of whether a sign of pathogen activity was recorded (1) or not (0).
None.Myc: A binary representation of whether a sign of myccorhizal activity was recorded (0) or not (1).
Mycorrhiza: The counterpart to the previous variable (None.Myc). A binary representation of whether a sign of mycorrhizal activity was recorded (1) or not (0).
None.Herb: A binary representation of whether herbivory was recorded (0) or not (1).
Herbivory: The counterpart to the previous variable (None.Herb). A binary representation of whether Herbivoryn was recorded (1) or not (0).
Population (pop): The coding number representing the population at which the sample was collected.
location: A code representing the whether the sample was collected inside a Alliaria petiolata population (I) or whther it was collected at least 7 m outside of he furthest individual in the A. petiolata population (O).
species: The particular species to which the sample belongs.
Cross: The particular cross number where the data was recorded on the individual sample.
Total scores:
indiv: The unique code given to a sample.
Decay: The total number of crosses where decay was recorded an individual sample when doing a total of 100 crosses/ sample.
Pathogen: The total number of crosses where pathogen was recorded on an individual sample when doing a total of 100 crosses/ sample.
Hyphae: The total number of crosses where non-myccorhizal hyphae was recorded on an individual sample when doing a total of 100 crosses/ sample.
None.Path: The total number of crosses where no signs of pathogen activities were recorded on an individual sample when doing a total of 100 crosses/ sample. Note that the total of Decay, Pathogen, Hyphae, and None.Path must come to 100 per individual to account for all 100 crosses.
Arbuscule: The total number of crosses where an arbuscule was recorded on an individual sample when doing a total of 100 crosses/ sample.
Vesicules: The total number of crosses where a vesicule was recorded on an individual sample when doing a total of 100 crosses/ sample.
M_Hyphae: The total number of crosses where myccorhizal hyphae was recorded on an individual sample when doing a total of 100 crosses/ sample.
None.Myc: The total number of crosses where no signs of mycorrhizal activities were recorded on an individual sample when doing a total of 100 crosses/ sample. Note that the total of Arbuscules, Vesicules, M_Hyphae, and None.Myc must come to 100 per individual to account for all 100 crosses.
Herbivory: The total number of crosses where herbivory was recorded on an individual sample when doing a total of 100 crosses/ sample.
None.Herb: The total number of crosses where no signs of herbivory was recorded on an individual sample when doing a total of 100 crosses/ sample. Note that the total of Herbivory, and None.Herb must come to 100 per individual to account for all 100 crosses.
Population (pop): The coding number representing the population at which the sample was collected.
location: A code representing the whether the sample was collected inside a Alliaria petiolata population (I) or whther it was collected at least 7 m outside of he furthest individual in the A. petiolata population (O).
species: The particular species to which the sample belongs.
Reviewing of hypotheses:
Question 1: Is there evidence that Mycorrhizal colonization provides protection against root pathogen damage?
Question 2: Do these effects vary among species?
Hypothesis 1
Mycorrhizal colonization protects roots from lesions and herbivory. 
Hypothesis 2
A. petiolata invasion reduces mycorrhizal colonization and increases pathogen colonization and herbivory 
### Hypothesis 3
Cycorrhizal colonization is reduced in the presence of A. petiolata 
Hypothesis 4
Mycorrhizal protection is completely lost in the presence of A. petiolata 
Molecular data Hypothesis
Hypothesis 1
A. petiolata invasion changes the diversity of mycorrhizal and other fungal species present in the soil.
I will find that the molecular data from the soil extraction supports this claim by having a reduced biodiversity and abundance of mycorrhiza in samples taken inside A. petiolata populations.
Hypothesis 2
There will be a negative correlation between mycorrhizal and fungal pathogen diversity.
Field Data Analysis
Plant length and GM presence
mod1<-PlantLength$Length_plant~PlantLength$Location+(1|PlantLength$Species)+(1|PlantLength$Population)
row.has.na <- apply(PlantLength, 1, function(x){any(is.na(x))})
sum(row.has.na) ## [1] 2PlantLength.filtered <- PlantLength[!row.has.na,]# Removed all the rows with NAs
mod1<-lmer(log(PlantLength.filtered$Length_plant)~PlantLength.filtered$Location+(1|PlantLength.filtered$Species)+(1|PlantLength.filtered$Population))
mod2<-lmer(log(PlantLength.filtered$Length_plant)~PlantLength.filtered$Location+(1|PlantLength.filtered$Species))
mod3<-lmer(log(PlantLength.filtered$Length_plant)~1+(1|PlantLength.filtered$Species)+(1|PlantLength.filtered$Population))
# Made these three models, one is all of them, one no population, and one no in/ out
summary(mod1)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## log(PlantLength.filtered$Length_plant) ~ PlantLength.filtered$Location +
## (1 | PlantLength.filtered$Species) + (1 | PlantLength.filtered$Population)
##
## REML criterion at convergence: 171.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1893 -0.6544 -0.0228 0.5866 2.5454
##
## Random effects:
## Groups Name Variance Std.Dev.
## PlantLength.filtered$Species (Intercept) 0.298185 0.54606
## PlantLength.filtered$Population (Intercept) 0.007485 0.08652
## Residual 0.102984 0.32091
## Number of obs: 229, groups:
## PlantLength.filtered$Species, 7; PlantLength.filtered$Population, 7
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.18352 0.21134 15.064
## PlantLength.filtered$Locationout -0.08492 0.04254 -1.996
##
## Correlation of Fixed Effects:
## (Intr)
## PlntLngt.$L -0.106anova(mod1,mod2) # One ANOVA with model 1, one with model 2 to compare if they are statistically significantly different from each other## refitting model(s) with ML (instead of REML)qplot(predict(mod1),log(PlantLength.filtered$Length_plant)) #is this model normal? NO
qplot(predict(mod1),log(PlantLength.filtered$Length_plant)-predict(mod1)) # Make this model normal by log() the y variable.
cor(predict(mod1),PlantLength.filtered$Length_plant)^2 # Are the correlation coefficients meaningful?## [1] 0.6185216cor(predict(mod2),PlantLength.filtered$Length_plant)^2 # Are the correlation coefficients meaningful wihout pops?## [1] 0.5985089anova(mod1,mod3) # Repeat with a model without the in/ out component.## refitting model(s) with ML (instead of REML)cor(predict(mod3),PlantLength.filtered$Length_plant)^2 # how much different does it make when we consider GM?## [1] 0.608331Floristic composition and GM presence
colnames(FloristicSurvey)[1] <- "Population" # population loads in weirdly, I am just arranging it to not have quotes around. so odd
FloristicSurvey$Population<-as.factor(FloristicSurvey$Population) # Make the population a factor and not an interger
FloristicSurvey[is.na(FloristicSurvey)] <- 0
sum(row.has.na <- apply(FloristicSurvey, 1, function(x){any(is.na(x))}))## [1] 0# Start the PCA
PC <- prcomp(FloristicSurvey[,4:ncol(FloristicSurvey)], center=T)
summary(PC)## Importance of components%s:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 0.6406 0.5639 0.49314 0.45065 0.42882 0.3954
## Proportion of Variance 0.1365 0.1058 0.08088 0.06755 0.06116 0.0520
## Cumulative Proportion 0.1365 0.2422 0.32311 0.39066 0.45182 0.5038
## PC7 PC8 PC9 PC10 PC11 PC12
## Standard deviation 0.37368 0.3608 0.34564 0.33141 0.30059 0.27972
## Proportion of Variance 0.04644 0.0433 0.03974 0.03653 0.03005 0.02602
## Cumulative Proportion 0.55027 0.5936 0.63330 0.66983 0.69989 0.72591
## PC13 PC14 PC15 PC16 PC17 PC18
## Standard deviation 0.26731 0.23707 0.23511 0.23170 0.23140 0.2159
## Proportion of Variance 0.02377 0.01869 0.01839 0.01786 0.01781 0.0155
## Cumulative Proportion 0.74968 0.76837 0.78675 0.80461 0.82242 0.8379
## PC19 PC20 PC21 PC22 PC23 PC24
## Standard deviation 0.20362 0.1992 0.1835 0.17727 0.17130 0.16138
## Proportion of Variance 0.01379 0.0132 0.0112 0.01045 0.00976 0.00866
## Cumulative Proportion 0.85171 0.8649 0.8761 0.88656 0.89632 0.90499
## PC25 PC26 PC27 PC28 PC29 PC30
## Standard deviation 0.16000 0.15304 0.14850 0.14015 0.13172 0.12966
## Proportion of Variance 0.00851 0.00779 0.00733 0.00653 0.00577 0.00559
## Cumulative Proportion 0.91350 0.92129 0.92863 0.93516 0.94093 0.94652
## PC31 PC32 PC33 PC34 PC35 PC36
## Standard deviation 0.12335 0.11774 0.11421 0.11329 0.10677 0.10455
## Proportion of Variance 0.00506 0.00461 0.00434 0.00427 0.00379 0.00364
## Cumulative Proportion 0.95158 0.95619 0.96053 0.96480 0.96859 0.97223
## PC37 PC38 PC39 PC40 PC41 PC42
## Standard deviation 0.10160 0.09716 0.09407 0.08205 0.07828 0.07736
## Proportion of Variance 0.00343 0.00314 0.00294 0.00224 0.00204 0.00199
## Cumulative Proportion 0.97566 0.97880 0.98174 0.98398 0.98602 0.98801
## PC43 PC44 PC45 PC46 PC47 PC48
## Standard deviation 0.07252 0.06984 0.06822 0.06603 0.06268 0.05955
## Proportion of Variance 0.00175 0.00162 0.00155 0.00145 0.00131 0.00118
## Cumulative Proportion 0.98976 0.99138 0.99293 0.99438 0.99569 0.99687
## PC49 PC50 PC51 PC52
## Standard deviation 0.05928 0.05691 0.05170 4.972e-17
## Proportion of Variance 0.00117 0.00108 0.00089 0.000e+00
## Cumulative Proportion 0.99803 0.99911 1.00000 1.000e+00screeplot(PC)
# Variation explaination
100*sum(summary(PC)[[1]][1])/sum(summary(PC)[[1]]) #explained by just PC1## [1] 6.330025100*sum(summary(PC)[[1]][1:2])/sum(summary(PC)[[1]])#explained by PC1 and PC2## [1] 11.90248n=25
100*sum(summary(PC)[[1]][1:n])/sum(summary(PC)[[1]])## [1] 75.49034Linear discriminate analysis
# Discriminant function analysis is used (general LDA format) because i have a cat. dependent and a binary independent. (it needs binary or continuous!)
# you might have to bin covers because it only works with categorical, so 0-5% none, 6-40 low etc.
FloristicSurvey$GM_Coverage_category<-cut(FloristicSurvey$GM_Coverage, c(-Inf,20,50,80,100), labels = c("None", "Med_Low", "Med_High", "Overtaken"))
table(FloristicSurvey$GM_Coverage_category)##
## None Med_Low Med_High Overtaken
## 80 26 72 20# [0-20] None
# ]20-50] Medium low
# ]50-80] Medium high
# ]80-100] OvertakenLDA
#LDA
FloristicSurveysmall<-data.frame(FloristicSurvey[,4:56])
# Linear discriminant function analysis
FloristicSurveysmall <- FloristicSurveysmall[,-c(42,45)]
FloristicSurveyLDA <- lda(GM_Coverage_category ~., data=FloristicSurveysmall)
# Extract scaling vectors
scalvec<-data.frame(FloristicSurveyLDA$scaling)
# Extract predictions
FloristicSurveyLDAval <- data.frame(predict(FloristicSurveyLDA)$x)
# Plot results
ggplot(data=FloristicSurveyLDAval,aes(x=LD1, y=LD2, group=FloristicSurveysmall$GM_Coverage_category))+
stat_ellipse(geom="polygon",aes(colour=FloristicSurveysmall$GM_Coverage_category),fill=NA,size=1.2,alpha=0.3)+
stat_ellipse(geom="polygon",aes(fill=FloristicSurveysmall$GM_Coverage_category,colour=FloristicSurveysmall$GM_Coverage_category),size=1.2,alpha=0.3)+
geom_point(aes(shape=FloristicSurveysmall$GM_Coverage_category,fill=FloristicSurveysmall$GM_Coverage_category,colour=FloristicSurveysmall$GM_Coverage_category),size=I(4),alpha=I(0.8))+
xlab("LD Axis 1")+ylab("LD Axis 2")+theme_simple() +
theme(legend.title=element_blank())
#test significance of axis
anova(lm(FloristicSurveyLDAval$LD1~FloristicSurveysmall$GM_Coverage_category))anova(lm(FloristicSurveyLDAval$LD2~FloristicSurveysmall$GM_Coverage_category))#LDA WITHOUT A. PETIOLATA
FloristicSurveysmall<-data.frame(FloristicSurvey[,4:56])
# Linear discriminant function analysis
FloristicSurveysmall[10]<-NULL
FloristicSurveysmall[c(41,44)] <- NULL
FloristicSurveyLDA<-lda(GM_Coverage_category ~ ., data=FloristicSurveysmall)
# Extract scaling vectors
scalvec<-data.frame(FloristicSurveyLDA$scaling)
# Extract predictions
FloristicSurveyLDAval <- data.frame(predict(FloristicSurveyLDA)$x)
# Plot results
ggplot(data=FloristicSurveyLDAval,aes(x=LD1,y=LD2,group=FloristicSurveysmall$GM_Coverage_category))+
stat_ellipse(geom="polygon",aes(colour=FloristicSurveysmall$GM_Coverage_category),fill=NA,size=1.2,alpha=0.3)+
stat_ellipse(geom="polygon",aes(fill=FloristicSurveysmall$GM_Coverage_category,colour=FloristicSurveysmall$GM_Coverage_category),size=1.2,alpha=0.3)+
geom_point(aes(shape=FloristicSurveysmall$GM_Coverage_category,fill=FloristicSurveysmall$GM_Coverage_category,colour=FloristicSurveysmall$GM_Coverage_category),size=I(4),alpha=I(0.8))+
xlab("LD Axis 1")+ylab("LD Axis 2")+theme_simple() +
theme(legend.title=element_blank())
#test significance of axis
anova(lm(FloristicSurveyLDAval$LD1~FloristicSurveysmall$GM_Coverage_category))anova(lm(FloristicSurveyLDAval$LD2~FloristicSurveysmall$GM_Coverage_category))Cluster analysis
# Ward Hierarchical Clustering with Bootstrapped p values
#do they cluster by population?
FloristicSurvey[is.na(FloristicSurvey)] <- 0
mydata<-t(data.frame(FloristicSurvey[,1],FloristicSurvey[,4:55]))
my.names <- mydata[1,]
colnames(mydata) <- my.names
mydata <- mydata[-1,]
d <- dist(t(mydata), method = "euclidean") # distance matrix
fit <- hclust(d, method = "ward.D")
plot(fit) 
#do they cluster by GM coverage?
FloristicSurvey[is.na(FloristicSurvey)] <- 0
#this will just make the dendogram easier to see
FloristicSurvey$GM_Coverage_category<-cut(FloristicSurvey$GM_Coverage, c(-Inf,5,30,50,70,95,100), labels = c("N", "L", "ML", "MH", "H", "F"))
mydata<-t(data.frame(FloristicSurvey[,56],FloristicSurvey[,4:55]))
my.names <- mydata[1,]
colnames(mydata) <- my.names
mydata <- mydata[-1,]
d <- dist(t(mydata), method = "euclidean") # distance matrix
fit <- hclust(d, method = "ward.D")
plot(fit) 
FloristicSurvey$GM_Coverage_category<-cut(FloristicSurvey$GM_Coverage, c(-Inf,5,30,50,70,95,100), labels = c("None", "Low", "Med_Low", "Med_High", "High", "Overtaken"))NMDS
# https://jonlefcheck.net/2012/10/24/nmds-tutorial-in-r/
# https://oliviarata.wordpress.com/2014/04/17/ordinations-in-ggplot2/
#Make a matrix with no row or column equal to 0 (do not enclude the env variable (GM COVERAGE))
M <- as.matrix(FloristicSurvey[1:198,4:55])
M[is.na(M)] <- 0
rownames(M) <- FloristicSurvey$Population
which( colSums(M)==0 )## Carpinus_carolinia
## 45which( rowSums(M)==0 )## 3 3
## 130 133#Now that you know which column must be taken out, redo the matrix but with the last column, then remove the rows and columns =0
#I did this because the previous method doesnt work with the characters in the GM_COVERAGE column.
M <- as.matrix(FloristicSurvey[1:198,4:56])
M[is.na(M)] <- 0
rownames(M) <- FloristicSurvey$Population
M<-M[,-45]
M<-M[-130,]
M<-M[-133,]
M<-M[-132,]
# Now I'll make the env column a vector on its own, but the previous colde now allows it to be in the same order as the matrix im using for distances.
GM_coverage_df <- data.frame(M[,52])
M<-M[,-52]
class(M) <- "numeric"
# with vegdist from Bray to seroeson: add binary = T
dist_FloristicSurvey <- vegdist(M, method = "bray", binary = T)
#The metaMDS analysis could have done the distance matrix internally but i would rather control it since i have presence/abscence
meta.nmds.FloristicSurvey <- metaMDS(dist_FloristicSurvey)## Run 0 stress 0.2097786
## Run 1 stress 0.2118606
## Run 2 stress 0.2097164
## ... New best solution
## ... Procrustes: rmse 0.00524235 max resid 0.04177558
## Run 3 stress 0.2170078
## Run 4 stress 0.2284479
## Run 5 stress 0.2096598
## ... New best solution
## ... Procrustes: rmse 0.005245703 max resid 0.05602814
## Run 6 stress 0.2098256
## ... Procrustes: rmse 0.01231086 max resid 0.1151435
## Run 7 stress 0.2170353
## Run 8 stress 0.2153965
## Run 9 stress 0.2116358
## Run 10 stress 0.2098729
## ... Procrustes: rmse 0.01331197 max resid 0.1361556
## Run 11 stress 0.215148
## Run 12 stress 0.2098735
## ... Procrustes: rmse 0.01263268 max resid 0.126724
## Run 13 stress 0.2116845
## Run 14 stress 0.2102258
## Run 15 stress 0.2126313
## Run 16 stress 0.2131586
## Run 17 stress 0.2131855
## Run 18 stress 0.2112311
## Run 19 stress 0.2096905
## ... Procrustes: rmse 0.009321867 max resid 0.1029974
## Run 20 stress 0.2132274
## *** No convergence -- monoMDS stopping criteria:
## 2: no. of iterations >= maxit
## 18: stress ratio > sratmax# Non convergence with only 20 tries. lets increase that then
meta.nmds.FloristicSurvey2D <- metaMDS(dist_FloristicSurvey, k=2, trymax = 1000)## Run 0 stress 0.2097786
## Run 1 stress 0.2112547
## Run 2 stress 0.2106852
## Run 3 stress 0.2208225
## Run 4 stress 0.2137372
## Run 5 stress 0.2097392
## ... New best solution
## ... Procrustes: rmse 0.00718742 max resid 0.0798187
## Run 6 stress 0.2124989
## Run 7 stress 0.2129202
## Run 8 stress 0.2137635
## Run 9 stress 0.2128476
## Run 10 stress 0.2125806
## Run 11 stress 0.2159597
## Run 12 stress 0.2103
## Run 13 stress 0.2098758
## ... Procrustes: rmse 0.009408093 max resid 0.1140905
## Run 14 stress 0.2145927
## Run 15 stress 0.2101736
## ... Procrustes: rmse 0.01217769 max resid 0.1131686
## Run 16 stress 0.2103604
## Run 17 stress 0.2182715
## Run 18 stress 0.213402
## Run 19 stress 0.2123159
## Run 20 stress 0.2097852
## ... Procrustes: rmse 0.005363804 max resid 0.05336445
## Run 21 stress 0.2098657
## ... Procrustes: rmse 0.009261906 max resid 0.1139693
## Run 22 stress 0.2101252
## ... Procrustes: rmse 0.009937061 max resid 0.09772294
## Run 23 stress 0.2098159
## ... Procrustes: rmse 0.009148565 max resid 0.1038414
## Run 24 stress 0.2097
## ... New best solution
## ... Procrustes: rmse 0.009823185 max resid 0.1036899
## Run 25 stress 0.2097555
## ... Procrustes: rmse 0.00814418 max resid 0.05827887
## Run 26 stress 0.2098755
## ... Procrustes: rmse 0.01357467 max resid 0.131995
## Run 27 stress 0.2404572
## Run 28 stress 0.2126283
## Run 29 stress 0.2100543
## ... Procrustes: rmse 0.007655709 max resid 0.07207129
## Run 30 stress 0.2123402
## Run 31 stress 0.2097392
## ... Procrustes: rmse 0.009641298 max resid 0.09381109
## Run 32 stress 0.212052
## Run 33 stress 0.2211139
## Run 34 stress 0.2101338
## ... Procrustes: rmse 0.008308897 max resid 0.07134837
## Run 35 stress 0.2147648
## Run 36 stress 0.2125887
## Run 37 stress 0.2100535
## ... Procrustes: rmse 0.007949393 max resid 0.07306144
## Run 38 stress 0.2125138
## Run 39 stress 0.2129366
## Run 40 stress 0.209854
## ... Procrustes: rmse 0.0118158 max resid 0.1315827
## Run 41 stress 0.2102893
## Run 42 stress 0.2126057
## Run 43 stress 0.2126647
## Run 44 stress 0.2176834
## Run 45 stress 0.2130861
## Run 46 stress 0.2101638
## ... Procrustes: rmse 0.01251173 max resid 0.1318302
## Run 47 stress 0.2102679
## Run 48 stress 0.2268205
## Run 49 stress 0.213238
## Run 50 stress 0.2098203
## ... Procrustes: rmse 0.008258257 max resid 0.1069386
## Run 51 stress 0.2137654
## Run 52 stress 0.2328722
## Run 53 stress 0.2101857
## ... Procrustes: rmse 0.01257772 max resid 0.1318834
## Run 54 stress 0.2133752
## Run 55 stress 0.2097745
## ... Procrustes: rmse 0.00464716 max resid 0.04011453
## Run 56 stress 0.2097129
## ... Procrustes: rmse 0.003910772 max resid 0.03913292
## Run 57 stress 0.2105312
## Run 58 stress 0.2129527
## Run 59 stress 0.2126595
## Run 60 stress 0.2147367
## Run 61 stress 0.2132329
## Run 62 stress 0.2126129
## Run 63 stress 0.2129796
## Run 64 stress 0.213264
## Run 65 stress 0.2125993
## Run 66 stress 0.2184764
## Run 67 stress 0.2098263
## ... Procrustes: rmse 0.009298469 max resid 0.1112046
## Run 68 stress 0.2158228
## Run 69 stress 0.2102315
## Run 70 stress 0.2097987
## ... Procrustes: rmse 0.01109859 max resid 0.1010329
## Run 71 stress 0.209743
## ... Procrustes: rmse 0.005797137 max resid 0.05459101
## Run 72 stress 0.212585
## Run 73 stress 0.20984
## ... Procrustes: rmse 0.0102877 max resid 0.1313941
## Run 74 stress 0.2098864
## ... Procrustes: rmse 0.01390775 max resid 0.1319615
## Run 75 stress 0.2098763
## ... Procrustes: rmse 0.0138568 max resid 0.1320641
## Run 76 stress 0.2098847
## ... Procrustes: rmse 0.01406611 max resid 0.1320731
## Run 77 stress 0.2102713
## Run 78 stress 0.2096615
## ... New best solution
## ... Procrustes: rmse 0.00692062 max resid 0.06139185
## Run 79 stress 0.2102652
## Run 80 stress 0.2185419
## Run 81 stress 0.2116849
## Run 82 stress 0.2217371
## Run 83 stress 0.2131764
## Run 84 stress 0.210468
## Run 85 stress 0.2147203
## Run 86 stress 0.2102534
## Run 87 stress 0.2117
## Run 88 stress 0.2134446
## Run 89 stress 0.2161576
## Run 90 stress 0.2133052
## Run 91 stress 0.2125821
## Run 92 stress 0.2160688
## Run 93 stress 0.2098391
## ... Procrustes: rmse 0.01124941 max resid 0.1243449
## Run 94 stress 0.212599
## Run 95 stress 0.2162705
## Run 96 stress 0.2101667
## Run 97 stress 0.2131857
## Run 98 stress 0.2098331
## ... Procrustes: rmse 0.009016082 max resid 0.1087286
## Run 99 stress 0.2098283
## ... Procrustes: rmse 0.01035589 max resid 0.1090343
## Run 100 stress 0.2408432
## Run 101 stress 0.209785
## ... Procrustes: rmse 0.01258053 max resid 0.1041663
## Run 102 stress 0.2191005
## Run 103 stress 0.2097177
## ... Procrustes: rmse 0.009468118 max resid 0.1010864
## Run 104 stress 0.2341083
## Run 105 stress 0.2096595
## ... New best solution
## ... Procrustes: rmse 0.002154158 max resid 0.01498952
## Run 106 stress 0.2096704
## ... Procrustes: rmse 0.002439552 max resid 0.02310321
## Run 107 stress 0.2133437
## Run 108 stress 0.2101521
## ... Procrustes: rmse 0.0141137 max resid 0.1179521
## Run 109 stress 0.2116398
## Run 110 stress 0.2155292
## Run 111 stress 0.2098694
## ... Procrustes: rmse 0.01248518 max resid 0.1157408
## Run 112 stress 0.2098212
## ... Procrustes: rmse 0.01237132 max resid 0.1141917
## Run 113 stress 0.2098833
## ... Procrustes: rmse 0.01397455 max resid 0.1356434
## Run 114 stress 0.2129437
## Run 115 stress 0.2129436
## Run 116 stress 0.2129478
## Run 117 stress 0.22287
## Run 118 stress 0.222658
## Run 119 stress 0.2098166
## ... Procrustes: rmse 0.01018018 max resid 0.1069602
## Run 120 stress 0.2116581
## Run 121 stress 0.2114843
## Run 122 stress 0.2274623
## Run 123 stress 0.2098432
## ... Procrustes: rmse 0.01016995 max resid 0.1125837
## Run 124 stress 0.2127465
## Run 125 stress 0.2132876
## Run 126 stress 0.2098845
## ... Procrustes: rmse 0.01314707 max resid 0.1138003
## Run 127 stress 0.2124702
## Run 128 stress 0.2102241
## Run 129 stress 0.2098111
## ... Procrustes: rmse 0.0124448 max resid 0.1081653
## Run 130 stress 0.2122607
## Run 131 stress 0.2097514
## ... Procrustes: rmse 0.005914794 max resid 0.04919618
## Run 132 stress 0.2126467
## Run 133 stress 0.2102318
## Run 134 stress 0.2125883
## Run 135 stress 0.2125245
## Run 136 stress 0.209883
## ... Procrustes: rmse 0.01390443 max resid 0.1327541
## Run 137 stress 0.2098289
## ... Procrustes: rmse 0.01112621 max resid 0.1195904
## Run 138 stress 0.2097547
## ... Procrustes: rmse 0.009033129 max resid 0.09424316
## Run 139 stress 0.2133042
## Run 140 stress 0.2102747
## Run 141 stress 0.2210968
## Run 142 stress 0.2117293
## Run 143 stress 0.2098413
## ... Procrustes: rmse 0.0102687 max resid 0.1130007
## Run 144 stress 0.2103063
## Run 145 stress 0.2096866
## ... Procrustes: rmse 0.004358966 max resid 0.03396607
## Run 146 stress 0.210277
## Run 147 stress 0.2098094
## ... Procrustes: rmse 0.009552282 max resid 0.1130953
## Run 148 stress 0.212472
## Run 149 stress 0.2147029
## Run 150 stress 0.214714
## Run 151 stress 0.2145465
## Run 152 stress 0.2098661
## ... Procrustes: rmse 0.01131578 max resid 0.1217265
## Run 153 stress 0.2146002
## Run 154 stress 0.2145566
## Run 155 stress 0.2101102
## ... Procrustes: rmse 0.006767511 max resid 0.07401685
## Run 156 stress 0.2371128
## Run 157 stress 0.210163
## Run 158 stress 0.2098206
## ... Procrustes: rmse 0.01223709 max resid 0.09602246
## Run 159 stress 0.2129292
## Run 160 stress 0.2107412
## Run 161 stress 0.2124858
## Run 162 stress 0.2102685
## Run 163 stress 0.2270066
## Run 164 stress 0.2097383
## ... Procrustes: rmse 0.01071446 max resid 0.09918804
## Run 165 stress 0.2098324
## ... Procrustes: rmse 0.01338536 max resid 0.1280022
## Run 166 stress 0.2098701
## ... Procrustes: rmse 0.01183182 max resid 0.1139977
## Run 167 stress 0.2097087
## ... Procrustes: rmse 0.009726719 max resid 0.09846339
## Run 168 stress 0.2133348
## Run 169 stress 0.2131409
## Run 170 stress 0.2144718
## Run 171 stress 0.2103159
## Run 172 stress 0.2116966
## Run 173 stress 0.2102693
## Run 174 stress 0.2102952
## Run 175 stress 0.2098208
## ... Procrustes: rmse 0.01305643 max resid 0.1247709
## Run 176 stress 0.2145722
## Run 177 stress 0.2101819
## Run 178 stress 0.2098768
## ... Procrustes: rmse 0.01373789 max resid 0.1330559
## Run 179 stress 0.2125205
## Run 180 stress 0.2124703
## Run 181 stress 0.2130273
## Run 182 stress 0.209707
## ... Procrustes: rmse 0.009498164 max resid 0.09529352
## Run 183 stress 0.2116569
## Run 184 stress 0.2097131
## ... Procrustes: rmse 0.008514103 max resid 0.09394618
## Run 185 stress 0.2098283
## ... Procrustes: rmse 0.01010459 max resid 0.09303508
## Run 186 stress 0.2216702
## Run 187 stress 0.2125068
## Run 188 stress 0.2097955
## ... Procrustes: rmse 0.01060585 max resid 0.09446631
## Run 189 stress 0.2126627
## Run 190 stress 0.2102923
## Run 191 stress 0.2097287
## ... Procrustes: rmse 0.01065612 max resid 0.09915962
## Run 192 stress 0.2138963
## Run 193 stress 0.2150085
## Run 194 stress 0.2097952
## ... Procrustes: rmse 0.01241158 max resid 0.1063897
## Run 195 stress 0.2148653
## Run 196 stress 0.2098759
## ... Procrustes: rmse 0.01379914 max resid 0.1313082
## Run 197 stress 0.2097728
## ... Procrustes: rmse 0.01295433 max resid 0.1173216
## Run 198 stress 0.216412
## Run 199 stress 0.2101222
## ... Procrustes: rmse 0.006336903 max resid 0.07082034
## Run 200 stress 0.2098156
## ... Procrustes: rmse 0.009739231 max resid 0.1128243
## Run 201 stress 0.2101529
## ... Procrustes: rmse 0.01085461 max resid 0.1133122
## Run 202 stress 0.2098338
## ... Procrustes: rmse 0.01352807 max resid 0.1268205
## Run 203 stress 0.2134306
## Run 204 stress 0.2348275
## Run 205 stress 0.2181281
## Run 206 stress 0.2101332
## ... Procrustes: rmse 0.007423958 max resid 0.06933705
## Run 207 stress 0.2097556
## ... Procrustes: rmse 0.008710169 max resid 0.1053688
## Run 208 stress 0.2098128
## ... Procrustes: rmse 0.009889361 max resid 0.08868194
## Run 209 stress 0.2097604
## ... Procrustes: rmse 0.007904933 max resid 0.1039547
## Run 210 stress 0.2120793
## Run 211 stress 0.2145861
## Run 212 stress 0.2098325
## ... Procrustes: rmse 0.01209831 max resid 0.126562
## Run 213 stress 0.2136885
## Run 214 stress 0.2116336
## Run 215 stress 0.2165315
## Run 216 stress 0.2129949
## Run 217 stress 0.2098327
## ... Procrustes: rmse 0.009456267 max resid 0.1125347
## Run 218 stress 0.212464
## Run 219 stress 0.2099212
## ... Procrustes: rmse 0.01503589 max resid 0.1498609
## Run 220 stress 0.2148993
## Run 221 stress 0.2177464
## Run 222 stress 0.210159
## ... Procrustes: rmse 0.01060139 max resid 0.1134212
## Run 223 stress 0.2174341
## Run 224 stress 0.2099154
## ... Procrustes: rmse 0.01357 max resid 0.1255281
## Run 225 stress 0.2102486
## Run 226 stress 0.21015
## ... Procrustes: rmse 0.01060009 max resid 0.09778667
## Run 227 stress 0.2101093
## ... Procrustes: rmse 0.007302969 max resid 0.07441789
## Run 228 stress 0.2215797
## Run 229 stress 0.2101241
## ... Procrustes: rmse 0.01085933 max resid 0.09926067
## Run 230 stress 0.2116692
## Run 231 stress 0.212948
## Run 232 stress 0.2098658
## ... Procrustes: rmse 0.01332571 max resid 0.123943
## Run 233 stress 0.2131357
## Run 234 stress 0.2120361
## Run 235 stress 0.2130986
## Run 236 stress 0.2132177
## Run 237 stress 0.2142634
## Run 238 stress 0.2099454
## ... Procrustes: rmse 0.0156032 max resid 0.1616617
## Run 239 stress 0.2098363
## ... Procrustes: rmse 0.01142511 max resid 0.1254833
## Run 240 stress 0.2098223
## ... Procrustes: rmse 0.01041371 max resid 0.1063697
## Run 241 stress 0.2102743
## Run 242 stress 0.2116766
## Run 243 stress 0.209737
## ... Procrustes: rmse 0.0102401 max resid 0.09836793
## Run 244 stress 0.2144918
## Run 245 stress 0.2102505
## Run 246 stress 0.210156
## ... Procrustes: rmse 0.006894339 max resid 0.07425289
## Run 247 stress 0.2150163
## Run 248 stress 0.2113171
## Run 249 stress 0.2125603
## Run 250 stress 0.212469
## Run 251 stress 0.2103005
## Run 252 stress 0.2096833
## ... Procrustes: rmse 0.01055223 max resid 0.09897283
## Run 253 stress 0.2097074
## ... Procrustes: rmse 0.009676704 max resid 0.09870454
## Run 254 stress 0.2098003
## ... Procrustes: rmse 0.013757 max resid 0.1205736
## Run 255 stress 0.2102656
## Run 256 stress 0.210165
## Run 257 stress 0.2325592
## Run 258 stress 0.2144453
## Run 259 stress 0.2125992
## Run 260 stress 0.2100826
## ... Procrustes: rmse 0.00688639 max resid 0.07421719
## Run 261 stress 0.2137323
## Run 262 stress 0.211697
## Run 263 stress 0.2131812
## Run 264 stress 0.2134174
## Run 265 stress 0.2101908
## Run 266 stress 0.2128276
## Run 267 stress 0.209868
## ... Procrustes: rmse 0.009805803 max resid 0.1118901
## Run 268 stress 0.2172628
## Run 269 stress 0.2124935
## Run 270 stress 0.2133038
## Run 271 stress 0.2098258
## ... Procrustes: rmse 0.01183162 max resid 0.1212858
## Run 272 stress 0.2148531
## Run 273 stress 0.2353518
## Run 274 stress 0.2132302
## Run 275 stress 0.2098314
## ... Procrustes: rmse 0.01122061 max resid 0.09745725
## Run 276 stress 0.2156803
## Run 277 stress 0.2129808
## Run 278 stress 0.2098189
## ... Procrustes: rmse 0.01194281 max resid 0.09562509
## Run 279 stress 0.2159205
## Run 280 stress 0.2116672
## Run 281 stress 0.2102496
## Run 282 stress 0.2132452
## Run 283 stress 0.2100655
## ... Procrustes: rmse 0.006814578 max resid 0.07312236
## Run 284 stress 0.2261394
## Run 285 stress 0.214567
## Run 286 stress 0.2098865
## ... Procrustes: rmse 0.01355715 max resid 0.1216802
## Run 287 stress 0.2130743
## Run 288 stress 0.2105431
## Run 289 stress 0.2121655
## Run 290 stress 0.2174596
## Run 291 stress 0.2133528
## Run 292 stress 0.2129535
## Run 293 stress 0.2101171
## ... Procrustes: rmse 0.006708617 max resid 0.07453036
## Run 294 stress 0.2235368
## Run 295 stress 0.2101417
## ... Procrustes: rmse 0.01129196 max resid 0.09899071
## Run 296 stress 0.2096765
## ... Procrustes: rmse 0.01015127 max resid 0.09877341
## Run 297 stress 0.2102547
## Run 298 stress 0.2253775
## Run 299 stress 0.2147179
## Run 300 stress 0.2169003
## Run 301 stress 0.2157152
## Run 302 stress 0.2103062
## Run 303 stress 0.2102764
## Run 304 stress 0.2149669
## Run 305 stress 0.2097999
## ... Procrustes: rmse 0.01148881 max resid 0.1102647
## Run 306 stress 0.210273
## Run 307 stress 0.2114726
## Run 308 stress 0.2103055
## Run 309 stress 0.2130008
## Run 310 stress 0.209774
## ... Procrustes: rmse 0.01071688 max resid 0.1322148
## Run 311 stress 0.2102439
## Run 312 stress 0.2238459
## Run 313 stress 0.2101094
## ... Procrustes: rmse 0.006316446 max resid 0.07323169
## Run 314 stress 0.2161524
## Run 315 stress 0.212902
## Run 316 stress 0.2121924
## Run 317 stress 0.2132344
## Run 318 stress 0.2097478
## ... Procrustes: rmse 0.003442987 max resid 0.02886923
## Run 319 stress 0.2134936
## Run 320 stress 0.2133612
## Run 321 stress 0.2101938
## Run 322 stress 0.2097201
## ... Procrustes: rmse 0.004828095 max resid 0.03427877
## Run 323 stress 0.2096708
## ... Procrustes: rmse 0.004766372 max resid 0.04152913
## Run 324 stress 0.2104983
## Run 325 stress 0.2180135
## Run 326 stress 0.2151474
## Run 327 stress 0.2149667
## Run 328 stress 0.2233816
## Run 329 stress 0.2102462
## Run 330 stress 0.2102764
## Run 331 stress 0.2166487
## Run 332 stress 0.2097506
## ... Procrustes: rmse 0.0111082 max resid 0.09923051
## Run 333 stress 0.2100734
## ... Procrustes: rmse 0.01114633 max resid 0.1260974
## Run 334 stress 0.2098872
## ... Procrustes: rmse 0.01418014 max resid 0.1408277
## Run 335 stress 0.2116357
## Run 336 stress 0.2140667
## Run 337 stress 0.2097803
## ... Procrustes: rmse 0.004390465 max resid 0.03171923
## Run 338 stress 0.2134122
## Run 339 stress 0.2116539
## Run 340 stress 0.2098687
## ... Procrustes: rmse 0.01298013 max resid 0.1138732
## Run 341 stress 0.2203287
## Run 342 stress 0.2097619
## ... Procrustes: rmse 0.009302973 max resid 0.09775453
## Run 343 stress 0.2096847
## ... Procrustes: rmse 0.01063181 max resid 0.09906337
## Run 344 stress 0.2147676
## Run 345 stress 0.226731
## Run 346 stress 0.216564
## Run 347 stress 0.2096761
## ... Procrustes: rmse 0.005010664 max resid 0.04394692
## Run 348 stress 0.2121353
## Run 349 stress 0.2112752
## Run 350 stress 0.2125621
## Run 351 stress 0.212163
## Run 352 stress 0.2098232
## ... Procrustes: rmse 0.01122232 max resid 0.1118926
## Run 353 stress 0.2146635
## Run 354 stress 0.2217151
## Run 355 stress 0.2098845
## ... Procrustes: rmse 0.01252086 max resid 0.1167795
## Run 356 stress 0.2150899
## Run 357 stress 0.211638
## Run 358 stress 0.2130409
## Run 359 stress 0.2134104
## Run 360 stress 0.2101554
## ... Procrustes: rmse 0.01083261 max resid 0.09878528
## Run 361 stress 0.2097181
## ... Procrustes: rmse 0.01049077 max resid 0.0990249
## Run 362 stress 0.2098301
## ... Procrustes: rmse 0.00926097 max resid 0.1120316
## Run 363 stress 0.2102157
## Run 364 stress 0.2140452
## Run 365 stress 0.2169991
## Run 366 stress 0.212611
## Run 367 stress 0.2133488
## Run 368 stress 0.2199419
## Run 369 stress 0.2102365
## Run 370 stress 0.2137365
## Run 371 stress 0.2099406
## ... Procrustes: rmse 0.01047812 max resid 0.1129201
## Run 372 stress 0.2102105
## Run 373 stress 0.2146606
## Run 374 stress 0.2098363
## ... Procrustes: rmse 0.01002951 max resid 0.1128423
## Run 375 stress 0.2102972
## Run 376 stress 0.212566
## Run 377 stress 0.2168887
## Run 378 stress 0.227929
## Run 379 stress 0.2165098
## Run 380 stress 0.2174999
## Run 381 stress 0.2105593
## Run 382 stress 0.2199012
## Run 383 stress 0.2144811
## Run 384 stress 0.2101337
## ... Procrustes: rmse 0.01049979 max resid 0.09812873
## Run 385 stress 0.2132895
## Run 386 stress 0.2098337
## ... Procrustes: rmse 0.01222055 max resid 0.1103748
## Run 387 stress 0.213875
## Run 388 stress 0.2122398
## Run 389 stress 0.2098329
## ... Procrustes: rmse 0.01309892 max resid 0.1247961
## Run 390 stress 0.2129427
## Run 391 stress 0.210164
## Run 392 stress 0.2102065
## Run 393 stress 0.2101834
## Run 394 stress 0.209848
## ... Procrustes: rmse 0.01024273 max resid 0.1126391
## Run 395 stress 0.2096781
## ... Procrustes: rmse 0.01004504 max resid 0.09877602
## Run 396 stress 0.210343
## Run 397 stress 0.210212
## Run 398 stress 0.2191958
## Run 399 stress 0.2133137
## Run 400 stress 0.2098878
## ... Procrustes: rmse 0.0139741 max resid 0.1332329
## Run 401 stress 0.2119699
## Run 402 stress 0.2101601
## Run 403 stress 0.2098225
## ... Procrustes: rmse 0.01051924 max resid 0.1058439
## Run 404 stress 0.2165482
## Run 405 stress 0.2102731
## Run 406 stress 0.2101015
## ... Procrustes: rmse 0.00583097 max resid 0.07021153
## Run 407 stress 0.2098087
## ... Procrustes: rmse 0.01306992 max resid 0.1220176
## Run 408 stress 0.2148146
## Run 409 stress 0.2096876
## ... Procrustes: rmse 0.01058089 max resid 0.09911439
## Run 410 stress 0.2097892
## ... Procrustes: rmse 0.007490779 max resid 0.09318147
## Run 411 stress 0.2130292
## Run 412 stress 0.2134101
## Run 413 stress 0.2098369
## ... Procrustes: rmse 0.009991527 max resid 0.113452
## Run 414 stress 0.2136995
## Run 415 stress 0.2096845
## ... Procrustes: rmse 0.002924546 max resid 0.01906487
## Run 416 stress 0.2098833
## ... Procrustes: rmse 0.01388903 max resid 0.1358856
## Run 417 stress 0.2101281
## ... Procrustes: rmse 0.01083026 max resid 0.09828001
## Run 418 stress 0.2151252
## Run 419 stress 0.2117031
## Run 420 stress 0.2107329
## Run 421 stress 0.2098218
## ... Procrustes: rmse 0.01301204 max resid 0.109759
## Run 422 stress 0.2129751
## Run 423 stress 0.2148817
## Run 424 stress 0.209928
## ... Procrustes: rmse 0.009877868 max resid 0.1130072
## Run 425 stress 0.2101561
## ... Procrustes: rmse 0.01133897 max resid 0.09872614
## Run 426 stress 0.2098262
## ... Procrustes: rmse 0.008287014 max resid 0.1003464
## Run 427 stress 0.2102782
## Run 428 stress 0.2133092
## Run 429 stress 0.210292
## Run 430 stress 0.2124555
## Run 431 stress 0.2206813
## Run 432 stress 0.2102762
## Run 433 stress 0.2103125
## Run 434 stress 0.2128136
## Run 435 stress 0.2102859
## Run 436 stress 0.2132208
## Run 437 stress 0.2258949
## Run 438 stress 0.2097383
## ... Procrustes: rmse 0.01111984 max resid 0.09858806
## Run 439 stress 0.2098313
## ... Procrustes: rmse 0.01090536 max resid 0.110615
## Run 440 stress 0.2097245
## ... Procrustes: rmse 0.00896737 max resid 0.09506139
## Run 441 stress 0.2098812
## ... Procrustes: rmse 0.01166169 max resid 0.1139626
## Run 442 stress 0.2098729
## ... Procrustes: rmse 0.01354766 max resid 0.1250313
## Run 443 stress 0.2102068
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## ... Procrustes: rmse 0.01112335 max resid 0.1134751
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## ... Procrustes: rmse 0.008712973 max resid 0.1126624
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## ... Procrustes: rmse 0.007554595 max resid 0.0543215
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## ... Procrustes: rmse 0.009113227 max resid 0.11116
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## ... Procrustes: rmse 0.01220602 max resid 0.1145546
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## ... Procrustes: rmse 0.009995158 max resid 0.09534522
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## ... Procrustes: rmse 0.01169932 max resid 0.1229044
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## ... Procrustes: rmse 0.00567013 max resid 0.07089248
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## ... Procrustes: rmse 0.0102838 max resid 0.09278108
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## ... Procrustes: rmse 0.01056589 max resid 0.09868389
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## ... Procrustes: rmse 0.01496649 max resid 0.1384985
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## ... Procrustes: rmse 0.01392064 max resid 0.1319699
## Run 489 stress 0.2129511
## Run 490 stress 0.2097241
## ... Procrustes: rmse 0.009260796 max resid 0.09515417
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## Run 494 stress 0.2098293
## ... Procrustes: rmse 0.009713215 max resid 0.1127126
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## ... Procrustes: rmse 0.01258209 max resid 0.1179552
## Run 496 stress 0.2100552
## ... Procrustes: rmse 0.006667917 max resid 0.07186998
## Run 497 stress 0.2218464
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## ... Procrustes: rmse 0.007238261 max resid 0.05666298
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## Run 501 stress 0.2126056
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## ... Procrustes: rmse 0.01232861 max resid 0.11741
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## ... Procrustes: rmse 0.01348859 max resid 0.1280534
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## Run 509 stress 0.2246319
## Run 510 stress 0.2102596
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## ... Procrustes: rmse 0.004433113 max resid 0.03929464
## Run 513 stress 0.2097068
## ... Procrustes: rmse 0.009824754 max resid 0.09575024
## Run 514 stress 0.2098107
## ... Procrustes: rmse 0.009370394 max resid 0.1134902
## Run 515 stress 0.2130006
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## ... Procrustes: rmse 0.01268227 max resid 0.1138048
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## Run 518 stress 0.2098942
## ... Procrustes: rmse 0.01405057 max resid 0.1377006
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## ... Procrustes: rmse 0.00995791 max resid 0.09832648
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## Run 523 stress 0.2101236
## ... Procrustes: rmse 0.008375699 max resid 0.06955491
## Run 524 stress 0.2209888
## Run 525 stress 0.2098637
## ... Procrustes: rmse 0.01322165 max resid 0.1228979
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## ... Procrustes: rmse 0.0112135 max resid 0.09913862
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## Run 528 stress 0.2133119
## Run 529 stress 0.2097641
## ... Procrustes: rmse 0.00328669 max resid 0.02486074
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## ... Procrustes: rmse 0.00744657 max resid 0.0565538
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## Run 532 stress 0.2097561
## ... Procrustes: rmse 0.009516546 max resid 0.09536615
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## Run 534 stress 0.2101555
## ... Procrustes: rmse 0.009425246 max resid 0.09380946
## Run 535 stress 0.2099311
## ... Procrustes: rmse 0.01211857 max resid 0.1150887
## Run 536 stress 0.2129333
## Run 537 stress 0.2098996
## ... Procrustes: rmse 0.01388681 max resid 0.1390573
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## Run 539 stress 0.2102852
## Run 540 stress 0.2103003
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## Run 546 stress 0.2113105
## Run 547 stress 0.2138326
## Run 548 stress 0.2103062
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## ... Procrustes: rmse 0.0131386 max resid 0.1128522
## Run 551 stress 0.2098996
## ... Procrustes: rmse 0.01354929 max resid 0.12633
## Run 552 stress 0.2134827
## Run 553 stress 0.2102233
## Run 554 stress 0.2133619
## Run 555 stress 0.21307
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## ... Procrustes: rmse 0.01335873 max resid 0.1194084
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## Run 560 stress 0.2101396
## ... Procrustes: rmse 0.007067692 max resid 0.07386116
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## ... Procrustes: rmse 0.009652608 max resid 0.1121361
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## Run 567 stress 0.2098213
## ... Procrustes: rmse 0.0130101 max resid 0.1160059
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## Run 570 stress 0.2116479
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## Run 572 stress 0.2103108
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## ... Procrustes: rmse 0.01023864 max resid 0.09875852
## Run 576 stress 0.2097514
## ... Procrustes: rmse 0.00739025 max resid 0.05302408
## Run 577 stress 0.2125916
## Run 578 stress 0.2098354
## ... Procrustes: rmse 0.01224141 max resid 0.1049909
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## ... Procrustes: rmse 0.006798774 max resid 0.07396568
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## ... Procrustes: rmse 0.008905729 max resid 0.1144188
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## Run 585 stress 0.2203195
## Run 586 stress 0.2176294
## Run 587 stress 0.2133886
## Run 588 stress 0.2098243
## ... Procrustes: rmse 0.01248189 max resid 0.117224
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## ... Procrustes: rmse 0.01376392 max resid 0.1320373
## Run 590 stress 0.212628
## Run 591 stress 0.2170228
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## ... Procrustes: rmse 0.009861282 max resid 0.1236078
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## Run 594 stress 0.2192589
## Run 595 stress 0.2138189
## Run 596 stress 0.2203743
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## ... Procrustes: rmse 0.01123969 max resid 0.1120439
## Run 599 stress 0.2105365
## Run 600 stress 0.2097506
## ... Procrustes: rmse 0.009449495 max resid 0.09823792
## Run 601 stress 0.2130849
## Run 602 stress 0.2098006
## ... Procrustes: rmse 0.009398278 max resid 0.1094274
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## Run 604 stress 0.2187382
## Run 605 stress 0.2101058
## ... Procrustes: rmse 0.006508794 max resid 0.07351697
## Run 606 stress 0.2117706
## Run 607 stress 0.2098805
## ... Procrustes: rmse 0.0121071 max resid 0.1138486
## Run 608 stress 0.2102228
## Run 609 stress 0.212214
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## ... Procrustes: rmse 0.003966494 max resid 0.03796427
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## ... Procrustes: rmse 0.01287611 max resid 0.1212562
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## Run 613 stress 0.2126015
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## ... Procrustes: rmse 0.01365958 max resid 0.1374179
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## ... Procrustes: rmse 0.003948496 max resid 0.0316665
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## Run 620 stress 0.2098829
## ... Procrustes: rmse 0.01343991 max resid 0.1326256
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## Run 622 stress 0.2102351
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## Run 624 stress 0.2101367
## ... Procrustes: rmse 0.0105621 max resid 0.09871279
## Run 625 stress 0.2146845
## Run 626 stress 0.2103098
## Run 627 stress 0.215058
## Run 628 stress 0.2179606
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## Run 630 stress 0.2131183
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## Run 633 stress 0.2112698
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## ... Procrustes: rmse 0.01266707 max resid 0.1143693
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## Run 636 stress 0.2097512
## ... Procrustes: rmse 0.007239067 max resid 0.05582716
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## Run 639 stress 0.2097613
## ... Procrustes: rmse 0.009878386 max resid 0.09558517
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## Run 642 stress 0.2102823
## Run 643 stress 0.2143019
## Run 644 stress 0.2165591
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## Run 655 stress 0.2133478
## Run 656 stress 0.2168372
## Run 657 stress 0.216567
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## Run 659 stress 0.2096758
## ... Procrustes: rmse 0.004386687 max resid 0.03875669
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## Run 661 stress 0.2101222
## ... Procrustes: rmse 0.01093279 max resid 0.09887241
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## ... Procrustes: rmse 0.01307202 max resid 0.1106987
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## Run 665 stress 0.2115749
## Run 666 stress 0.2118875
## Run 667 stress 0.2133668
## Run 668 stress 0.2112687
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## ... Procrustes: rmse 0.005199624 max resid 0.04626864
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## Run 673 stress 0.2116411
## Run 674 stress 0.2132183
## Run 675 stress 0.2102158
## Run 676 stress 0.2101818
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## Run 678 stress 0.209726
## ... Procrustes: rmse 0.005668511 max resid 0.04343082
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## Run 681 stress 0.2097953
## ... Procrustes: rmse 0.01091975 max resid 0.1013251
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## Run 683 stress 0.2122097
## Run 684 stress 0.2098177
## ... Procrustes: rmse 0.01036717 max resid 0.09324884
## Run 685 stress 0.2101629
## Run 686 stress 0.2098527
## ... Procrustes: rmse 0.00861048 max resid 0.1125584
## Run 687 stress 0.2148762
## Run 688 stress 0.2146983
## Run 689 stress 0.2099187
## ... Procrustes: rmse 0.01353557 max resid 0.1315924
## Run 690 stress 0.2098406
## ... Procrustes: rmse 0.01370917 max resid 0.1308513
## Run 691 stress 0.2099621
## ... Procrustes: rmse 0.01314241 max resid 0.1197407
## Run 692 stress 0.2124713
## Run 693 stress 0.2098684
## ... Procrustes: rmse 0.01307463 max resid 0.1269314
## Run 694 stress 0.213849
## Run 695 stress 0.2112407
## Run 696 stress 0.2133916
## Run 697 stress 0.2102695
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## Run 699 stress 0.2224951
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## ... Procrustes: rmse 0.001064338 max resid 0.01039364
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## ... Procrustes: rmse 0.003137598 max resid 0.02738151
## Run 702 stress 0.2157909
## Run 703 stress 0.2125736
## Run 704 stress 0.2129893
## Run 705 stress 0.2098479
## ... Procrustes: rmse 0.01019898 max resid 0.1125492
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## Run 707 stress 0.2129139
## Run 708 stress 0.2115072
## Run 709 stress 0.2177483
## Run 710 stress 0.2131668
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## Run 713 stress 0.2172744
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## ... Procrustes: rmse 0.01012026 max resid 0.1125063
## Run 715 stress 0.2097645
## ... Procrustes: rmse 0.01228445 max resid 0.1057485
## Run 716 stress 0.2163647
## Run 717 stress 0.2097315
## ... Procrustes: rmse 0.004638391 max resid 0.02975934
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## Run 719 stress 0.2102299
## Run 720 stress 0.2101822
## Run 721 stress 0.2101891
## Run 722 stress 0.2147016
## Run 723 stress 0.2101189
## ... Procrustes: rmse 0.007964828 max resid 0.06936149
## Run 724 stress 0.2175506
## Run 725 stress 0.2098643
## ... Procrustes: rmse 0.01326766 max resid 0.1236441
## Run 726 stress 0.2179765
## Run 727 stress 0.2121183
## Run 728 stress 0.2098688
## ... Procrustes: rmse 0.01272242 max resid 0.1210226
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## Run 730 stress 0.2097576
## ... Procrustes: rmse 0.01000468 max resid 0.1192852
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## Run 732 stress 0.2133866
## Run 733 stress 0.2103247
## Run 734 stress 0.2136471
## Run 735 stress 0.2135083
## Run 736 stress 0.2098744
## ... Procrustes: rmse 0.01367328 max resid 0.1304632
## Run 737 stress 0.2123359
## Run 738 stress 0.209876
## ... Procrustes: rmse 0.0135356 max resid 0.1222613
## Run 739 stress 0.2125567
## Run 740 stress 0.2125471
## Run 741 stress 0.2101942
## Run 742 stress 0.2097434
## ... Procrustes: rmse 0.007620573 max resid 0.05657957
## Run 743 stress 0.2130308
## Run 744 stress 0.2101334
## ... Procrustes: rmse 0.01097001 max resid 0.09814399
## Run 745 stress 0.2133995
## Run 746 stress 0.2160963
## Run 747 stress 0.2132863
## Run 748 stress 0.209972
## ... Procrustes: rmse 0.01356242 max resid 0.1287512
## Run 749 stress 0.2101236
## ... Procrustes: rmse 0.007954414 max resid 0.06943498
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## ... Procrustes: rmse 0.01334148 max resid 0.1268681
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## Run 752 stress 0.2147929
## Run 753 stress 0.2101707
## Run 754 stress 0.2096807
## ... Procrustes: rmse 0.004103403 max resid 0.03588827
## Run 755 stress 0.213447
## Run 756 stress 0.2113295
## Run 757 stress 0.2124826
## Run 758 stress 0.2176852
## Run 759 stress 0.213415
## Run 760 stress 0.2122851
## Run 761 stress 0.2212595
## Run 762 stress 0.2096978
## ... Procrustes: rmse 0.009229628 max resid 0.0953311
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## Run 764 stress 0.2226695
## Run 765 stress 0.2299467
## Run 766 stress 0.2128666
## Run 767 stress 0.2160498
## Run 768 stress 0.2195187
## Run 769 stress 0.2096948
## ... Procrustes: rmse 0.005953409 max resid 0.05176567
## Run 770 stress 0.2146362
## Run 771 stress 0.2097326
## ... Procrustes: rmse 0.01106645 max resid 0.09903854
## Run 772 stress 0.2166668
## Run 773 stress 0.2147922
## Run 774 stress 0.2128825
## Run 775 stress 0.2099357
## ... Procrustes: rmse 0.01125035 max resid 0.1148871
## Run 776 stress 0.2097934
## ... Procrustes: rmse 0.012659 max resid 0.1040199
## Run 777 stress 0.2112719
## Run 778 stress 0.2130767
## Run 779 stress 0.2102953
## Run 780 stress 0.2114606
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## ... Procrustes: rmse 0.01296009 max resid 0.1138902
## Run 782 stress 0.2097301
## ... Procrustes: rmse 0.005984004 max resid 0.05298279
## Run 783 stress 0.2097357
## ... Procrustes: rmse 0.01083969 max resid 0.09930591
## Run 784 stress 0.2098297
## ... Procrustes: rmse 0.01080947 max resid 0.1078383
## Run 785 stress 0.2098907
## ... Procrustes: rmse 0.01233384 max resid 0.114803
## Run 786 stress 0.2131558
## Run 787 stress 0.2097781
## ... Procrustes: rmse 0.01188473 max resid 0.102094
## Run 788 stress 0.2164021
## Run 789 stress 0.2098214
## ... Procrustes: rmse 0.01022317 max resid 0.1083471
## Run 790 stress 0.2098736
## ... Procrustes: rmse 0.01355002 max resid 0.1234737
## Run 791 stress 0.2102802
## Run 792 stress 0.2123186
## Run 793 stress 0.2161973
## Run 794 stress 0.2098166
## ... Procrustes: rmse 0.01335928 max resid 0.1254515
## Run 795 stress 0.2144305
## Run 796 stress 0.2126993
## Run 797 stress 0.2098219
## ... Procrustes: rmse 0.01004642 max resid 0.1125127
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## Run 799 stress 0.2097876
## ... Procrustes: rmse 0.01201141 max resid 0.1106461
## Run 800 stress 0.2134448
## Run 801 stress 0.2102826
## Run 802 stress 0.2132248
## Run 803 stress 0.2173746
## Run 804 stress 0.2144933
## Run 805 stress 0.2230081
## Run 806 stress 0.2126217
## Run 807 stress 0.2176444
## Run 808 stress 0.2271627
## Run 809 stress 0.2102893
## Run 810 stress 0.2098678
## ... Procrustes: rmse 0.01294458 max resid 0.1155142
## Run 811 stress 0.2097821
## ... Procrustes: rmse 0.01385073 max resid 0.1230284
## Run 812 stress 0.216071
## Run 813 stress 0.2236648
## Run 814 stress 0.2140888
## Run 815 stress 0.2097933
## ... Procrustes: rmse 0.01216414 max resid 0.1040005
## Run 816 stress 0.2184702
## Run 817 stress 0.2098343
## ... Procrustes: rmse 0.01336807 max resid 0.1255584
## Run 818 stress 0.2098744
## ... Procrustes: rmse 0.01347646 max resid 0.1281541
## Run 819 stress 0.2129783
## Run 820 stress 0.2123422
## Run 821 stress 0.2097871
## ... Procrustes: rmse 0.01243963 max resid 0.1156342
## Run 822 stress 0.2097893
## ... Procrustes: rmse 0.01215267 max resid 0.1125725
## Run 823 stress 0.2117471
## Run 824 stress 0.2097047
## ... Procrustes: rmse 0.006414172 max resid 0.05232136
## Run 825 stress 0.2101821
## Run 826 stress 0.2138174
## Run 827 stress 0.2100938
## ... Procrustes: rmse 0.01144888 max resid 0.1141101
## Run 828 stress 0.2097529
## ... Procrustes: rmse 0.009653697 max resid 0.09563189
## Run 829 stress 0.2096639
## ... Procrustes: rmse 0.001667789 max resid 0.0131327
## Run 830 stress 0.2099331
## ... Procrustes: rmse 0.009404259 max resid 0.1133689
## Run 831 stress 0.2180702
## Run 832 stress 0.2242779
## Run 833 stress 0.2096629
## ... Procrustes: rmse 0.00210631 max resid 0.01522735
## Run 834 stress 0.2222526
## Run 835 stress 0.2102597
## Run 836 stress 0.2158543
## Run 837 stress 0.2098646
## ... Procrustes: rmse 0.01182586 max resid 0.1146054
## Run 838 stress 0.2098088
## ... Procrustes: rmse 0.01386649 max resid 0.1153057
## Run 839 stress 0.2098256
## ... Procrustes: rmse 0.009527889 max resid 0.1121889
## Run 840 stress 0.2098165
## ... Procrustes: rmse 0.01091257 max resid 0.1132212
## Run 841 stress 0.2137009
## Run 842 stress 0.2127002
## Run 843 stress 0.2097136
## ... Procrustes: rmse 0.006723851 max resid 0.05528988
## Run 844 stress 0.2308826
## Run 845 stress 0.2199156
## Run 846 stress 0.209756
## ... Procrustes: rmse 0.01009308 max resid 0.09849361
## Run 847 stress 0.2129637
## Run 848 stress 0.2112354
## Run 849 stress 0.2163042
## Run 850 stress 0.2201199
## Run 851 stress 0.2101092
## ... Procrustes: rmse 0.006682506 max resid 0.07357681
## Run 852 stress 0.2102935
## Run 853 stress 0.2118575
## Run 854 stress 0.2101759
## Run 855 stress 0.2136656
## Run 856 stress 0.2254043
## Run 857 stress 0.2097498
## ... Procrustes: rmse 0.008828452 max resid 0.1080643
## Run 858 stress 0.2180322
## Run 859 stress 0.215366
## Run 860 stress 0.209882
## ... Procrustes: rmse 0.01385542 max resid 0.1330181
## Run 861 stress 0.2129379
## Run 862 stress 0.2098826
## ... Procrustes: rmse 0.01384001 max resid 0.130788
## Run 863 stress 0.2131054
## Run 864 stress 0.2097754
## ... Procrustes: rmse 0.01212088 max resid 0.1119183
## Run 865 stress 0.2133504
## Run 866 stress 0.2133863
## Run 867 stress 0.2098874
## ... Procrustes: rmse 0.01409695 max resid 0.137601
## Run 868 stress 0.2121934
## Run 869 stress 0.2097386
## ... Procrustes: rmse 0.008153115 max resid 0.09374947
## Run 870 stress 0.210266
## Run 871 stress 0.2097684
## ... Procrustes: rmse 0.01333438 max resid 0.1182951
## Run 872 stress 0.2102723
## Run 873 stress 0.2098276
## ... Procrustes: rmse 0.01322426 max resid 0.1283852
## Run 874 stress 0.2102053
## Run 875 stress 0.2129794
## Run 876 stress 0.2097542
## ... Procrustes: rmse 0.01104338 max resid 0.0986199
## Run 877 stress 0.2134099
## Run 878 stress 0.2129573
## Run 879 stress 0.2129824
## Run 880 stress 0.2098298
## ... Procrustes: rmse 0.01263921 max resid 0.1179243
## Run 881 stress 0.2102495
## Run 882 stress 0.2101509
## ... Procrustes: rmse 0.01067218 max resid 0.09828677
## Run 883 stress 0.2097982
## ... Procrustes: rmse 0.01270636 max resid 0.1130211
## Run 884 stress 0.2098408
## ... Procrustes: rmse 0.01372478 max resid 0.1271599
## Run 885 stress 0.2199901
## Run 886 stress 0.2098343
## ... Procrustes: rmse 0.01026003 max resid 0.1125524
## Run 887 stress 0.2097135
## ... Procrustes: rmse 0.0065404 max resid 0.05041735
## Run 888 stress 0.220841
## Run 889 stress 0.2121718
## Run 890 stress 0.2145736
## Run 891 stress 0.2102713
## Run 892 stress 0.2131175
## Run 893 stress 0.209814
## ... Procrustes: rmse 0.009840559 max resid 0.1128721
## Run 894 stress 0.2096696
## ... Procrustes: rmse 0.004444276 max resid 0.04196895
## Run 895 stress 0.212127
## Run 896 stress 0.2116384
## Run 897 stress 0.212472
## Run 898 stress 0.2098858
## ... Procrustes: rmse 0.01415194 max resid 0.1384793
## Run 899 stress 0.2126071
## Run 900 stress 0.21289
## Run 901 stress 0.2120337
## Run 902 stress 0.2097171
## ... Procrustes: rmse 0.009536104 max resid 0.09542711
## Run 903 stress 0.2125786
## Run 904 stress 0.2129556
## Run 905 stress 0.2116836
## Run 906 stress 0.2133044
## Run 907 stress 0.2096878
## ... Procrustes: rmse 0.009311335 max resid 0.09817816
## Run 908 stress 0.2124906
## Run 909 stress 0.2128701
## Run 910 stress 0.2132509
## Run 911 stress 0.2098739
## ... Procrustes: rmse 0.0137181 max resid 0.1325362
## Run 912 stress 0.210116
## ... Procrustes: rmse 0.006449523 max resid 0.07322291
## Run 913 stress 0.2129641
## Run 914 stress 0.2101999
## Run 915 stress 0.2112876
## Run 916 stress 0.216283
## Run 917 stress 0.2131026
## Run 918 stress 0.2097183
## ... Procrustes: rmse 0.01040086 max resid 0.09885583
## Run 919 stress 0.2230509
## Run 920 stress 0.2134593
## Run 921 stress 0.2101266
## ... Procrustes: rmse 0.01091151 max resid 0.09855517
## Run 922 stress 0.2098015
## ... Procrustes: rmse 0.01190137 max resid 0.09826269
## Run 923 stress 0.2242289
## Run 924 stress 0.2202579
## Run 925 stress 0.2128869
## Run 926 stress 0.2103286
## Run 927 stress 0.2126258
## Run 928 stress 0.2173053
## Run 929 stress 0.2098777
## ... Procrustes: rmse 0.01184396 max resid 0.1144778
## Run 930 stress 0.2116584
## Run 931 stress 0.2243239
## Run 932 stress 0.2098194
## ... Procrustes: rmse 0.009328302 max resid 0.112201
## Run 933 stress 0.2153703
## Run 934 stress 0.209889
## ... Procrustes: rmse 0.01414107 max resid 0.1362336
## Run 935 stress 0.2153822
## Run 936 stress 0.2096685
## ... Procrustes: rmse 0.001726747 max resid 0.01456804
## Run 937 stress 0.2129479
## Run 938 stress 0.2097257
## ... Procrustes: rmse 0.0105934 max resid 0.09918761
## Run 939 stress 0.2113066
## Run 940 stress 0.2134383
## Run 941 stress 0.2132259
## Run 942 stress 0.2127133
## Run 943 stress 0.2097755
## ... Procrustes: rmse 0.009776879 max resid 0.1139626
## Run 944 stress 0.2096945
## ... Procrustes: rmse 0.01040407 max resid 0.09904312
## Run 945 stress 0.2129204
## Run 946 stress 0.2242187
## Run 947 stress 0.2134914
## Run 948 stress 0.210116
## ... Procrustes: rmse 0.006384516 max resid 0.07336787
## Run 949 stress 0.2098328
## ... Procrustes: rmse 0.01353015 max resid 0.120206
## Run 950 stress 0.2147839
## Run 951 stress 0.2137019
## Run 952 stress 0.2124964
## Run 953 stress 0.2096931
## ... Procrustes: rmse 0.01072479 max resid 0.09878907
## Run 954 stress 0.2209515
## Run 955 stress 0.2216707
## Run 956 stress 0.2098121
## ... Procrustes: rmse 0.01007834 max resid 0.1174334
## Run 957 stress 0.2098663
## ... Procrustes: rmse 0.01338016 max resid 0.1253382
## Run 958 stress 0.2132827
## Run 959 stress 0.2103063
## Run 960 stress 0.2099595
## ... Procrustes: rmse 0.01248918 max resid 0.1135436
## Run 961 stress 0.215346
## Run 962 stress 0.2103209
## Run 963 stress 0.2277915
## Run 964 stress 0.2130794
## Run 965 stress 0.2192446
## Run 966 stress 0.209772
## ... Procrustes: rmse 0.01350762 max resid 0.1197548
## Run 967 stress 0.2176923
## Run 968 stress 0.2128034
## Run 969 stress 0.224562
## Run 970 stress 0.2121562
## Run 971 stress 0.2098111
## ... Procrustes: rmse 0.009508489 max resid 0.1132301
## Run 972 stress 0.2096771
## ... Procrustes: rmse 0.01029215 max resid 0.09887659
## Run 973 stress 0.2135696
## Run 974 stress 0.2098916
## ... Procrustes: rmse 0.01217843 max resid 0.1138886
## Run 975 stress 0.2129745
## Run 976 stress 0.2124869
## Run 977 stress 0.21041
## Run 978 stress 0.2098757
## ... Procrustes: rmse 0.01365951 max resid 0.1253434
## Run 979 stress 0.209715
## ... Procrustes: rmse 0.008923703 max resid 0.09520818
## Run 980 stress 0.2125045
## Run 981 stress 0.2125826
## Run 982 stress 0.2126617
## Run 983 stress 0.2096769
## ... Procrustes: rmse 0.002537145 max resid 0.01586817
## Run 984 stress 0.2098214
## ... Procrustes: rmse 0.009560405 max resid 0.111947
## Run 985 stress 0.2121464
## Run 986 stress 0.2128249
## Run 987 stress 0.2198862
## Run 988 stress 0.21167
## Run 989 stress 0.2101536
## ... Procrustes: rmse 0.01094475 max resid 0.1132663
## Run 990 stress 0.2103213
## Run 991 stress 0.2097708
## ... Procrustes: rmse 0.01346718 max resid 0.1151883
## Run 992 stress 0.2157162
## Run 993 stress 0.2251516
## Run 994 stress 0.2101384
## ... Procrustes: rmse 0.01042577 max resid 0.09837933
## Run 995 stress 0.2098753
## ... Procrustes: rmse 0.01270207 max resid 0.1139496
## Run 996 stress 0.2098751
## ... Procrustes: rmse 0.01271014 max resid 0.1139581
## Run 997 stress 0.2102304
## Run 998 stress 0.214995
## Run 999 stress 0.212579
## Run 1000 stress 0.2098148
## ... Procrustes: rmse 0.009875996 max resid 0.1130735
## *** No convergence -- monoMDS stopping criteria:
## 55: no. of iterations >= maxit
## 945: stress ratio > sratmaxstr(meta.nmds.FloristicSurvey2D)## List of 35
## $ nobj : int 195
## $ nfix : int 0
## $ ndim : num 2
## $ ndis : int 18915
## $ ngrp : int 1
## $ diss : num [1:18915] 0 0 0 0 0 0 0 0 0 0 ...
## $ iidx : int [1:18915] 114 105 114 67 119 131 89 97 111 111 ...
## $ jidx : int [1:18915] 100 103 112 2 101 120 55 56 103 105 ...
## $ xinit : num [1:390] 0.923 0.826 0.269 0.991 0.27 ...
## $ istart : int 1
## $ isform : int 1
## $ ities : int 1
## $ iregn : int 1
## $ iscal : int 1
## $ maxits : int 200
## $ sratmx : num 1
## $ strmin : num 1e-04
## $ sfgrmn : num 1e-07
## $ dist : num [1:18915] 0 0 0 0 0 0 0 0 0 0 ...
## $ dhat : num [1:18915] 0 0 0 0 0 0 0 0 0 0 ...
## $ points : num [1:195, 1:2] -0.132 -0.147 -0.158 -0.105 -0.106 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:195] "7" "7" "7" "7" ...
## .. ..$ : chr [1:2] "MDS1" "MDS2"
## ..- attr(*, "centre")= logi TRUE
## ..- attr(*, "pc")= logi TRUE
## ..- attr(*, "halfchange")= logi FALSE
## ..- attr(*, "internalscaling")= num 4.31
## $ stress : num 0.21
## $ grstress : num 0.21
## $ iters : int 81
## $ icause : int 3
## $ call : language metaMDS(comm = dist_FloristicSurvey, k = 2, trymax = 1000)
## $ model : chr "global"
## $ distmethod: chr "binary bray"
## $ distcall : chr "vegdist(x = M, method = \"bray\", binary = T)"
## $ distance : chr "binary bray"
## $ converged : logi FALSE
## $ tries : num 1000
## $ engine : chr "monoMDS"
## $ species : logi NA
## $ data : chr "dist_FloristicSurvey"
## - attr(*, "class")= chr [1:2] "metaMDS" "monoMDS"stressplot(meta.nmds.FloristicSurvey2D)
# Im getting a little above a stress of 0.2 (0.207), which isnt ideal, ill try it again with 3 dimension
# A good rule of thumb: stress < 0.05 provides an excellent representation in reduced dimensions, < 0.1 is great, < 0.2 is good/ok, and stress < 0.3 provides a poor representation.
meta.nmds.FloristicSurvey3D <- metaMDS(dist_FloristicSurvey, k=3, trymax = 1000)## Run 0 stress 0.1472339
## Run 1 stress 0.147845
## Run 2 stress 0.1486126
## Run 3 stress 0.1478375
## Run 4 stress 0.1481742
## Run 5 stress 0.1488738
## Run 6 stress 0.1475808
## ... Procrustes: rmse 0.01567161 max resid 0.09041528
## Run 7 stress 0.1482255
## Run 8 stress 0.1482442
## Run 9 stress 0.1560041
## Run 10 stress 0.1486371
## Run 11 stress 0.1495387
## Run 12 stress 0.1495404
## Run 13 stress 0.1478405
## Run 14 stress 0.1478471
## Run 15 stress 0.1488738
## Run 16 stress 0.1475676
## ... Procrustes: rmse 0.01450191 max resid 0.0902353
## Run 17 stress 0.1482355
## Run 18 stress 0.1481492
## Run 19 stress 0.1473331
## ... Procrustes: rmse 0.006800388 max resid 0.08686157
## Run 20 stress 0.1599306
## Run 21 stress 0.1483659
## Run 22 stress 0.1475892
## ... Procrustes: rmse 0.01650029 max resid 0.1128641
## Run 23 stress 0.1559226
## Run 24 stress 0.1488719
## Run 25 stress 0.1475837
## ... Procrustes: rmse 0.01795506 max resid 0.1228054
## Run 26 stress 0.1475107
## ... Procrustes: rmse 0.0136737 max resid 0.09045298
## Run 27 stress 0.1476433
## ... Procrustes: rmse 0.01914247 max resid 0.1191426
## Run 28 stress 0.1475539
## ... Procrustes: rmse 0.01439849 max resid 0.08985557
## Run 29 stress 0.1495296
## Run 30 stress 0.147409
## ... Procrustes: rmse 0.0112789 max resid 0.08844544
## Run 31 stress 0.1475074
## ... Procrustes: rmse 0.01333346 max resid 0.0898477
## Run 32 stress 0.1478596
## Run 33 stress 0.1472993
## ... Procrustes: rmse 0.004283632 max resid 0.05498272
## Run 34 stress 0.1484736
## Run 35 stress 0.1482754
## Run 36 stress 0.1476378
## ... Procrustes: rmse 0.01933188 max resid 0.1218889
## Run 37 stress 0.1478675
## Run 38 stress 0.1476816
## ... Procrustes: rmse 0.007256092 max resid 0.07654745
## Run 39 stress 0.1488672
## Run 40 stress 0.1482427
## Run 41 stress 0.1482503
## Run 42 stress 0.1472241
## ... New best solution
## ... Procrustes: rmse 0.001932235 max resid 0.02491834
## Run 43 stress 0.1485225
## Run 44 stress 0.1498813
## Run 45 stress 0.1478506
## Run 46 stress 0.1482473
## Run 47 stress 0.1478505
## Run 48 stress 0.1478506
## Run 49 stress 0.1477885
## Run 50 stress 0.1488635
## Run 51 stress 0.1480955
## Run 52 stress 0.1479838
## Run 53 stress 0.148247
## Run 54 stress 0.147642
## ... Procrustes: rmse 0.02013675 max resid 0.1417831
## Run 55 stress 0.1477791
## Run 56 stress 0.1476386
## ... Procrustes: rmse 0.02014269 max resid 0.1411722
## Run 57 stress 0.1478376
## Run 58 stress 0.1476366
## ... Procrustes: rmse 0.02008467 max resid 0.1398935
## Run 59 stress 0.1477258
## Run 60 stress 0.1473111
## ... Procrustes: rmse 0.005676916 max resid 0.0757508
## Run 61 stress 0.1488656
## Run 62 stress 0.1479689
## Run 63 stress 0.147652
## ... Procrustes: rmse 0.019882 max resid 0.1398833
## Run 64 stress 0.1476399
## ... Procrustes: rmse 0.02003299 max resid 0.139002
## Run 65 stress 0.1481721
## Run 66 stress 0.1482412
## Run 67 stress 0.1493593
## Run 68 stress 0.1493694
## Run 69 stress 0.1487477
## Run 70 stress 0.1476472
## ... Procrustes: rmse 0.01260785 max resid 0.1293964
## Run 71 stress 0.1488716
## Run 72 stress 0.1478596
## Run 73 stress 0.1476167
## ... Procrustes: rmse 0.006229479 max resid 0.07636218
## Run 74 stress 0.1477052
## ... Procrustes: rmse 0.009303682 max resid 0.09618332
## Run 75 stress 0.1475537
## ... Procrustes: rmse 0.01458862 max resid 0.09027303
## Run 76 stress 0.1478654
## Run 77 stress 0.1476396
## ... Procrustes: rmse 0.02012063 max resid 0.1407968
## Run 78 stress 0.1473797
## ... Procrustes: rmse 0.01156493 max resid 0.08887696
## Run 79 stress 0.1476288
## ... Procrustes: rmse 0.01946082 max resid 0.1303855
## Run 80 stress 0.1478377
## Run 81 stress 0.148258
## Run 82 stress 0.1488708
## Run 83 stress 0.1486851
## Run 84 stress 0.1473641
## ... Procrustes: rmse 0.006385749 max resid 0.0779665
## Run 85 stress 0.1479572
## Run 86 stress 0.1488641
## Run 87 stress 0.1473808
## ... Procrustes: rmse 0.01152497 max resid 0.08849104
## Run 88 stress 0.1502107
## Run 89 stress 0.1476014
## ... Procrustes: rmse 0.01885987 max resid 0.1200633
## Run 90 stress 0.147853
## Run 91 stress 0.147225
## ... Procrustes: rmse 0.001203653 max resid 0.01530389
## Run 92 stress 0.1483518
## Run 93 stress 0.1473131
## ... Procrustes: rmse 0.005617756 max resid 0.07306795
## Run 94 stress 0.1475587
## ... Procrustes: rmse 0.01049257 max resid 0.1023251
## Run 95 stress 0.1476265
## ... Procrustes: rmse 0.01932061 max resid 0.1247804
## Run 96 stress 0.1483915
## Run 97 stress 0.1488612
## Run 98 stress 0.1478565
## Run 99 stress 0.1490258
## Run 100 stress 0.1482512
## Run 101 stress 0.1488695
## Run 102 stress 0.1476655
## ... Procrustes: rmse 0.01251478 max resid 0.13848
## Run 103 stress 0.1472422
## ... Procrustes: rmse 0.002494852 max resid 0.01920491
## Run 104 stress 0.1474824
## ... Procrustes: rmse 0.009127591 max resid 0.0881224
## Run 105 stress 0.147839
## Run 106 stress 0.1485395
## Run 107 stress 0.1478554
## Run 108 stress 0.1516947
## Run 109 stress 0.1478487
## Run 110 stress 0.1474187
## ... Procrustes: rmse 0.01212465 max resid 0.08884664
## Run 111 stress 0.1478355
## Run 112 stress 0.1610461
## Run 113 stress 0.1476989
## ... Procrustes: rmse 0.008899706 max resid 0.08909242
## Run 114 stress 0.1488678
## Run 115 stress 0.1473363
## ... Procrustes: rmse 0.00674508 max resid 0.08908845
## Run 116 stress 0.1475096
## ... Procrustes: rmse 0.01679961 max resid 0.124777
## Run 117 stress 0.1482799
## Run 118 stress 0.1483455
## Run 119 stress 0.1495422
## Run 120 stress 0.1478503
## Run 121 stress 0.1489577
## Run 122 stress 0.147365
## ... Procrustes: rmse 0.01123406 max resid 0.08880898
## Run 123 stress 0.1476199
## ... Procrustes: rmse 0.006211334 max resid 0.07651768
## Run 124 stress 0.1478622
## Run 125 stress 0.1558743
## Run 126 stress 0.1499354
## Run 127 stress 0.1486993
## Run 128 stress 0.147367
## ... Procrustes: rmse 0.007656135 max resid 0.0948792
## Run 129 stress 0.1485442
## Run 130 stress 0.1494129
## Run 131 stress 0.1474786
## ... Procrustes: rmse 0.00915178 max resid 0.08337381
## Run 132 stress 0.1488589
## Run 133 stress 0.1476417
## ... Procrustes: rmse 0.02013721 max resid 0.1416759
## Run 134 stress 0.1478677
## Run 135 stress 0.1481001
## Run 136 stress 0.149644
## Run 137 stress 0.1472951
## ... Procrustes: rmse 0.0031719 max resid 0.02892864
## Run 138 stress 0.1475794
## ... Procrustes: rmse 0.01599062 max resid 0.09043829
## Run 139 stress 0.1488631
## Run 140 stress 0.1476282
## ... Procrustes: rmse 0.01999698 max resid 0.1335971
## Run 141 stress 0.1493906
## Run 142 stress 0.1487143
## Run 143 stress 0.1480024
## Run 144 stress 0.1480977
## Run 145 stress 0.1476439
## ... Procrustes: rmse 0.02037032 max resid 0.1396773
## Run 146 stress 0.1479813
## Run 147 stress 0.1482298
## Run 148 stress 0.1482598
## Run 149 stress 0.1475631
## ... Procrustes: rmse 0.0110457 max resid 0.1040098
## Run 150 stress 0.1493688
## Run 151 stress 0.1558621
## Run 152 stress 0.1482623
## Run 153 stress 0.14927
## Run 154 stress 0.1479646
## Run 155 stress 0.1483403
## Run 156 stress 0.1480465
## Run 157 stress 0.1474963
## ... Procrustes: rmse 0.01742518 max resid 0.1316828
## Run 158 stress 0.1482441
## Run 159 stress 0.1477645
## Run 160 stress 0.1481983
## Run 161 stress 0.1482449
## Run 162 stress 0.1504534
## Run 163 stress 0.1475056
## ... Procrustes: rmse 0.01510194 max resid 0.09849841
## Run 164 stress 0.1486575
## Run 165 stress 0.148687
## Run 166 stress 0.1480975
## Run 167 stress 0.1476385
## ... Procrustes: rmse 0.02025962 max resid 0.138872
## Run 168 stress 0.1495316
## Run 169 stress 0.1488603
## Run 170 stress 0.1481157
## Run 171 stress 0.147841
## Run 172 stress 0.148778
## Run 173 stress 0.1483677
## Run 174 stress 0.1472299
## ... Procrustes: rmse 0.001881896 max resid 0.01508081
## Run 175 stress 0.1488624
## Run 176 stress 0.149037
## Run 177 stress 0.1475687
## ... Procrustes: rmse 0.01799899 max resid 0.1323855
## Run 178 stress 0.1481801
## Run 179 stress 0.1488658
## Run 180 stress 0.1474777
## ... Procrustes: rmse 0.01018975 max resid 0.09644619
## Run 181 stress 0.147649
## ... Procrustes: rmse 0.0201017 max resid 0.1404399
## Run 182 stress 0.1479897
## Run 183 stress 0.1484493
## Run 184 stress 0.1476406
## ... Procrustes: rmse 0.02015337 max resid 0.1414342
## Run 185 stress 0.1474469
## ... Procrustes: rmse 0.01627604 max resid 0.1200323
## Run 186 stress 0.1476485
## ... Procrustes: rmse 0.01766931 max resid 0.1275618
## Run 187 stress 0.147629
## ... Procrustes: rmse 0.01921176 max resid 0.1277295
## Run 188 stress 0.1479617
## Run 189 stress 0.1475411
## ... Procrustes: rmse 0.007082833 max resid 0.08423845
## Run 190 stress 0.1478458
## Run 191 stress 0.1472301
## ... Procrustes: rmse 0.001070434 max resid 0.01152145
## Run 192 stress 0.1475719
## ... Procrustes: rmse 0.01812416 max resid 0.1301772
## Run 193 stress 0.1478348
## Run 194 stress 0.1488717
## Run 195 stress 0.1475772
## ... Procrustes: rmse 0.01096053 max resid 0.1040352
## Run 196 stress 0.1485018
## Run 197 stress 0.14745
## ... Procrustes: rmse 0.01665081 max resid 0.1270779
## Run 198 stress 0.1476284
## ... Procrustes: rmse 0.005986012 max resid 0.07631243
## Run 199 stress 0.1481318
## Run 200 stress 0.1478354
## Run 201 stress 0.1487709
## Run 202 stress 0.148459
## Run 203 stress 0.1475696
## ... Procrustes: rmse 0.01801853 max resid 0.1323743
## Run 204 stress 0.1473517
## ... Procrustes: rmse 0.00591432 max resid 0.06865051
## Run 205 stress 0.147501
## ... Procrustes: rmse 0.01019194 max resid 0.1008233
## Run 206 stress 0.1472389
## ... Procrustes: rmse 0.001975834 max resid 0.01501376
## Run 207 stress 0.147639
## ... Procrustes: rmse 0.02004943 max resid 0.1342263
## Run 208 stress 0.1476199
## ... Procrustes: rmse 0.01876498 max resid 0.1186053
## Run 209 stress 0.1481048
## Run 210 stress 0.147236
## ... Procrustes: rmse 0.001066494 max resid 0.009984632
## ... Similar to previous best
## *** Solution reachedstr(meta.nmds.FloristicSurvey3D)## List of 35
## $ nobj : int 195
## $ nfix : int 0
## $ ndim : num 3
## $ ndis : int 18915
## $ ngrp : int 1
## $ diss : num [1:18915] 0 0 0 0 0 0 0 0 0 0 ...
## $ iidx : int [1:18915] 111 67 111 97 105 112 89 114 115 177 ...
## $ jidx : int [1:18915] 103 2 105 56 103 94 55 59 100 118 ...
## $ xinit : num [1:585] 0.376 0.603 0.299 0.296 0.619 ...
## $ istart : int 1
## $ isform : int 1
## $ ities : int 1
## $ iregn : int 1
## $ iscal : int 1
## $ maxits : int 200
## $ sratmx : num 1
## $ strmin : num 1e-04
## $ sfgrmn : num 1e-07
## $ dist : num [1:18915] 0 0 0 0 0 ...
## $ dhat : num [1:18915] 0 0 0 0 0 ...
## $ points : num [1:195, 1:3] -0.1448 -0.1579 -0.1309 -0.102 -0.0905 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:195] "7" "7" "7" "7" ...
## .. ..$ : chr [1:3] "MDS1" "MDS2" "MDS3"
## ..- attr(*, "centre")= logi TRUE
## ..- attr(*, "pc")= logi TRUE
## ..- attr(*, "halfchange")= logi FALSE
## ..- attr(*, "internalscaling")= num 3.57
## $ stress : num 0.147
## $ grstress : num 0.147
## $ iters : int 96
## $ icause : int 3
## $ call : language metaMDS(comm = dist_FloristicSurvey, k = 3, trymax = 1000)
## $ model : chr "global"
## $ distmethod: chr "binary bray"
## $ distcall : chr "vegdist(x = M, method = \"bray\", binary = T)"
## $ distance : chr "binary bray"
## $ converged : logi TRUE
## $ tries : num 210
## $ engine : chr "monoMDS"
## $ species : logi NA
## $ data : chr "dist_FloristicSurvey"
## - attr(*, "class")= chr [1:2] "metaMDS" "monoMDS"# stress is lower! 0.146
stressplot(meta.nmds.FloristicSurvey3D)
# envfit for the 2D
FloristicSurvey_envfit <- envfit(meta.nmds.FloristicSurvey2D, env = GM_coverage_df, perm = 999) #standard envfit
FloristicSurvey_envfit##
## ***FACTORS:
##
## Centroids:
## NMDS1 NMDS2
## M...52.High 0.0306 0.0250
## M...52.Low -0.0089 -0.0028
## M...52.Med_High 0.0776 -0.0008
## M...52.Med_Low 0.0566 0.0444
## M...52.None -0.1409 -0.0359
## M...52.Overtaken 0.1643 0.0624
##
## Goodness of fit:
## r2 Pr(>r)
## M...52. 0.1681 0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Permutation: free
## Number of permutations: 999#data for plotting
##NMDS points
FloristicSurvey.NMDS.data<-GM_coverage_df
FloristicSurvey.NMDS.data$NMDS1<-meta.nmds.FloristicSurvey2D$points[ ,1]
FloristicSurvey.NMDS.data$NMDS2<-meta.nmds.FloristicSurvey2D$points[ ,2]
colnames(FloristicSurvey.NMDS.data)[1] <- "GM_Coverage"
# data for the envfit arrows
env.scores.FloristicSurvey <- as.data.frame(scores(FloristicSurvey_envfit, display = "vectors")) #extracts relevant scores from envifit
env.scores.FloristicSurvey <- cbind(env.scores.FloristicSurvey, env.variables = rownames(env.scores.FloristicSurvey)) #and then gives them their names
# function for ellipsess - just run this, is used later
#taken from the excellent stackoverflow Q+A: http://stackoverflow.com/questions/13794419/plotting-ordiellipse-function-from-vegan-package-onto-nmds-plot-created-in-ggplo
veganCovEllipse <- function (cov, center = c(0, 0), scale = 1, npoints = 100)
{
theta <- (0:npoints) * 2 * pi/npoints
Circle <- cbind(cos(theta), sin(theta))
t(center + scale * t(Circle %*% chol(cov)))
}
#data for ellipse, use GM coverage
df_ell.FSurvey.GM_coverage <- data.frame() #sets up a data frame before running the function.
for(g in levels(FloristicSurvey.NMDS.data$GM_Coverage)){
df_ell.FSurvey.GM_coverage <- rbind(df_ell.FSurvey.GM_coverage, cbind(as.data.frame(with(FloristicSurvey.NMDS.data [FloristicSurvey.NMDS.data$GM_Coverage==g,],
veganCovEllipse(cov.wt(cbind(NMDS1,NMDS2),wt=rep(1/length(NMDS1),length(NMDS1)))$cov,center=c(mean(NMDS1),mean(NMDS2)))))
,GM_coverage=g))
}
# data for labelling the ellipse
NMDS.mean.FloristicSurvey=aggregate(FloristicSurvey.NMDS.data[ ,c("NMDS1", "NMDS2")],
list(group = FloristicSurvey.NMDS.data$GM_Coverage), mean)
## finally plotting.
mult <- 1 #multiplier for the arrows and text for envfit below. You can change this and then rerun the plot command.
FloristicSurvey.nmds.gg1 <- ggplot(data = FloristicSurvey.NMDS.data, aes(y = NMDS2, x = NMDS1))+ #sets up the plot. brackets around the entire thing to make it draw automatically
geom_path(data = df_ell.FSurvey.GM_coverage, aes(x = NMDS1, y = NMDS2, group = df_ell.FSurvey.GM_coverage$GM_coverage, alpha=df_ell.FSurvey.GM_coverage$GM_coverage))+ #this is the ellipse, seperate ones by Site. If you didn't change the "alpha" (the shade) then you need to keep the "group
scale_alpha_manual(guide = FALSE,values=c(0.3, 0.5, 0.6, 0.7, 0.8, 0.9))+ #sets the shade for the ellipse
geom_point( aes(shape = FloristicSurvey.NMDS.data$GM_Coverage), size = 1) + #puts the site points in from the ordination, shape determined by site, size refers to size of point
# geom_text(data=spps2, aes(x=spps2$NMDS1, y=spps2$NMDS2, label=species), size = 3.3, hjust=1.1)+ #labelling the species. hjust used to shift them slightly from their points
#annotate("text",x = NMDS.mean$NMDS1,y = NMDS.mean$NMDS2,label=NMDS.mean$group) + #labels for the centroids - I haven't used this since we have a legend. but you could also dithc the legend, but plot will get v messy
#geom_segment(data = env.scores.FloristicSurvey,
# aes(x = 0, xend = mult*env.scores.FloristicSurvey$NMDS1, y = 0, yend = mult*env.scores.FloristicSurvey$NMDS2),
# arrow = arrow(length = unit(0.25, "cm")), colour = "grey") + #arrows for envfit. doubled the length for similarity to the plot() function. NB check ?envfit regarding arrow length if not familiar with lengths
#geom_text(data = env.scores.FloristicSurvey, #labels the environmental variable arrows * "mult" as for the arrows
# aes(x = mult*env.scores.FloristicSurvey$NMDS1, y = mult*env.scores.FloristicSurvey$NMDS2, label=env.variables),
# size = 5,
# hjust = -0.5)+
scale_shape_manual(values = c(1,8,19,5,6,7))+ #sets the shape of the plot points instead of using whatever ggplot2 automatically provides
coord_cartesian(xlim = c(-1,1.5))+ ## NB this changes the visible area of the plot only (this is a good thing, apparently). Can also specify ylim. Here in case you want to set xaxis manually.
theme_simple()Soil Characteristics
Soil_characteristics$Location<-as.factor(Soil_characteristics$Location)
GLmodel_soil <- glm(Location ~Agg_stability*C_percent*N_percent,family=binomial(link='logit'),data=Soil_characteristics)## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurredsummary(GLmodel_soil)##
## Call:
## glm(formula = Location ~ Agg_stability * C_percent * N_percent,
## family = binomial(link = "logit"), data = Soil_characteristics)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5019 -0.9103 -0.1493 0.7927 2.1777
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -40.68 40.25 -1.011 0.312
## Agg_stability 57.36 62.43 0.919 0.358
## C_percent 28.40 18.23 1.558 0.119
## N_percent -178.24 138.30 -1.289 0.197
## Agg_stability:C_percent -40.73 26.92 -1.513 0.130
## Agg_stability:N_percent 253.80 211.09 1.202 0.229
## C_percent:N_percent -14.38 10.04 -1.432 0.152
## Agg_stability:C_percent:N_percent 20.95 15.18 1.380 0.168
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 27.726 on 19 degrees of freedom
## Residual deviance: 18.370 on 12 degrees of freedom
## AIC: 34.37
##
## Number of Fisher Scoring iterations: 8Soil_characteristics2 <- data.frame(Soil_characteristics$Population, Soil_characteristics$Location, log(Soil_characteristics$pH), log(Soil_characteristics$Agg_stability), log(Soil_characteristics$C_percent), log(Soil_characteristics$N_percent))
Soil_characteristics2<-rename(Soil_characteristics2, c("Soil_characteristics.Population"="Population", "Soil_characteristics.Location"="Location", "log.Soil_characteristics.pH."="pH", "log.Soil_characteristics.Agg_stability."="Agg_stability", "log.Soil_characteristics.C_percent."="Percent","log.Soil_characteristics.N_percent."="Percent" ))## Warning: The plyr::rename operation has created duplicates for the
## following name(s): (`Percent`)df2 <- reshape2::melt(Soil_characteristics2, id.var=c("Population","Location"))
df2 <- rename(df2, c("value"="Log_value"))
p <- ggplot(Soil_characteristics, aes(Location,pH,fill=Location))
p + geom_boxplot() +
theme_simple()
# Histology data Analysis
Data exploration
Calculate plant-level Mycchorizae, pathogens and herbivory:
# Fix column characteristics for plotting and analysis
fdata$indiv2<-as.factor(fdata$indiv2)
fdata$Mycorrhiza<-as.numeric(paste(fdata$Mycorrhiza))
fdata$Lesion<-as.numeric(paste(fdata$Lesion))
fdata$Herbivory<-as.numeric(paste(fdata$Herbivory))
pct<-function(x){
sum(x)/100
}
# Calculate plant-level averages
fdat_ind<-aggregate(fdata[,c("Mycorrhiza","Lesion","Herbivory")],by=list(indiv2=fdata$indiv2,pop=fdata$pop,loc=fdata$loc,species=fdata$species), FUN=pct)Simple linear model visualization:
## Mycorrhiza model (NOTE: No loc*species because not all species present in all populations)
base.Myc<-lmer(Mycorrhiza~species+loc+species:loc+(1|pop)+(1|pop:loc),data=fdat_ind)
noint.Myc<-lmer(Mycorrhiza~species+loc+(1|pop)+(1|pop:loc),data=fdat_ind)
anova(base.Myc,noint.Myc)## refitting model(s) with ML (instead of REML)base.Myc ## Inspect coefficients## Linear mixed model fit by REML ['lmerMod']
## Formula:
## Mycorrhiza ~ species + loc + species:loc + (1 | pop) + (1 | pop:loc)
## Data: fdat_ind
## REML criterion at convergence: -12.5748
## Random effects:
## Groups Name Std.Dev.
## pop:loc (Intercept) 0.06622
## pop (Intercept) 0.00000
## Residual 0.21042
## Number of obs: 225, groups: pop:loc, 22; pop, 11
## Fixed Effects:
## (Intercept) speciesCL speciesGA speciesGR
## 0.38985 -0.05067 0.03105 0.01338
## speciesMR speciesSC locO speciesCL:locO
## -0.02840 0.28780 0.15278 0.13277
## speciesGA:locO speciesGR:locO speciesMR:locO speciesSC:locO
## -0.10069 0.23077 0.28893 -0.04707ggplot(fdat_ind,aes(species,Mycorrhiza,colour=loc))+geom_boxplot()+theme_simple()
ggplot(fdat_ind,aes(pop,Mycorrhiza,colour=loc))+geom_boxplot()+theme_simple()
Mycorrhia model results
- Mycorrhiza colonization is significantly higher outside patches of A. petiolata than inside 2a. Species vary in Mycorrhiza colonization, with highest colonization in SC and others relatively similar. 2b. Effect of A. petiolata on Mycorrhiza colonization differs among species, with more pronounced effects for GR and MR, and will little effect for GA
- Effect of A. petiolata on Mycorrhiza colonization varies by population, but not as strongly as among species
## Mycorrhiza model (NOTE: No loc*species because not all species present in all populations)
base.Les<-lmer(Lesion~Mycorrhiza*species*loc+(1|pop/loc),data=fdat_ind)
norint.Les<-lmer(Lesion~Mycorrhiza*species*loc+(1|pop),data=fdat_ind)
anova(base.Les,norint.Les)## refitting model(s) with ML (instead of REML)norint.Les # inspect coefficients## Linear mixed model fit by REML ['lmerMod']
## Formula: Lesion ~ Mycorrhiza * species * loc + (1 | pop)
## Data: fdat_ind
## REML criterion at convergence: -70.9219
## Random effects:
## Groups Name Std.Dev.
## pop (Intercept) 0.04934
## Residual 0.18543
## Number of obs: 225, groups: pop, 11
## Fixed Effects:
## (Intercept) Mycorrhiza
## 0.686711 0.053896
## speciesCL speciesGA
## -0.188794 0.146342
## speciesGR speciesMR
## 0.090499 -0.310235
## speciesSC locO
## -0.037506 0.016259
## Mycorrhiza:speciesCL Mycorrhiza:speciesGA
## 0.216958 -0.702730
## Mycorrhiza:speciesGR Mycorrhiza:speciesMR
## -0.020628 0.559261
## Mycorrhiza:speciesSC Mycorrhiza:locO
## 0.136864 -0.056951
## speciesCL:locO speciesGA:locO
## -0.225004 -0.389157
## speciesGR:locO speciesMR:locO
## -0.565486 -0.129568
## speciesSC:locO Mycorrhiza:speciesCL:locO
## -0.007965 0.098911
## Mycorrhiza:speciesGA:locO Mycorrhiza:speciesGR:locO
## 0.784046 0.433494
## Mycorrhiza:speciesMR:locO Mycorrhiza:speciesSC:locO
## -0.172551 -0.051787Les2<-lmer(Lesion~Mycorrhiza*species*loc-Mycorrhiza:species:loc+(1|pop),data=fdat_ind)
anova(norint.Les,Les2)## refitting model(s) with ML (instead of REML)Les3a<-lmer(Lesion~Mycorrhiza*species+Mycorrhiza*loc+(1|pop),data=fdat_ind)
Les3b<-lmer(Lesion~Mycorrhiza*species+species*loc+(1|pop),data=fdat_ind)
Les3c<-lmer(Lesion~species*loc+Mycorrhiza*loc+(1|pop),data=fdat_ind)
anova(norint.Les,Les3a) # TEST species*loc ## refitting model(s) with ML (instead of REML)anova(norint.Les,Les3b) # TEST Myc*loc ## refitting model(s) with ML (instead of REML)anova(norint.Les,Les3c) # TEST Myc*species## refitting model(s) with ML (instead of REML)ggplot(fdat_ind,aes(Mycorrhiza,Lesion))+facet_wrap(~species)+
geom_point(aes(col=loc))+theme_simple()+geom_smooth(method="lm")
** Lesions model results**
- Root lesions increase with mycorrhiza colonization, contrary to predictions
- Effect of Mycorrhiza on Lesions depends strongly on species (Myc*species interactions)
Hypothesis 1: Lesion ~ Mycorriza
GIVEN THE NEW ANALYSIS ABOVE, THIS ISN’T WORTHWILE BECAUSE THERE IS NO SIGNIFICANT Myc:species:loc
# calculating the r
indivCODE <- unique(fdata$indiv2)
dfcorr <-data.frame(indivCODE=c(0),r=c(0))
for (i in 1:length(indivCODE)){
dat1<-NULL
dat1<-filter(fdata, fdata$indiv2==indivCODE[i])
dfcorr[i,1] <- indivCODE[i]
dfcorr[i,2] <- cor(as.numeric(dat1$Mycorrhiza),as.numeric(dat1$Lesion))
}## Warning in cor(as.numeric(dat1$Mycorrhiza), as.numeric(dat1$Lesion)): the
## standard deviation is zero
## Warning in cor(as.numeric(dat1$Mycorrhiza), as.numeric(dat1$Lesion)): the
## standard deviation is zero
## Warning in cor(as.numeric(dat1$Mycorrhiza), as.numeric(dat1$Lesion)): the
## standard deviation is zero
## Warning in cor(as.numeric(dat1$Mycorrhiza), as.numeric(dat1$Lesion)): the
## standard deviation is zero
## Warning in cor(as.numeric(dat1$Mycorrhiza), as.numeric(dat1$Lesion)): the
## standard deviation is zero
## Warning in cor(as.numeric(dat1$Mycorrhiza), as.numeric(dat1$Lesion)): the
## standard deviation is zerodfcorr %>% drop_na()->dfcorrCo-occurence data
#Normal?
car::qqp(dfcorr$r, "norm")
shapiro.test(dfcorr$r)
hist(dfcorr$r)
# Cannot be normal because it is only between -1 and 1 and our mean is at 0.
descdist(dfcorr$r, discrete = FALSE, boot = 500)
# weibull when transformed to be positive?
dfcorr$r.t <- dfcorr$r+1
fit.weibull <- fitdist(dfcorr$r.t, "weibull")
car::qqp(dfcorr$r.t, "weibull", shape = fit.weibull$estimate[[1]])
dfcorr$pop <- gsub("^([0-9]+)[I,O][A-Z]+.*","\\1",dfcorr$indivCODE)
dfcorr$location <- gsub("^[0-9]+([I,O])[A-Z]+.*","\\1",dfcorr$indivCODE)
dfcorr$species <- sub("^[0-9]+[I,O]([A-Z]+).*","\\1",dfcorr$indivCODE)
dfcorr$location <- as.factor(dfcorr$location)
dfcorr$species <- as.factor(dfcorr$species)
dfcorr$pop <- as.factor(dfcorr$pop)
meanR<-mean(dfcorr$r)
SEMR<-sd(dfcorr$r)/sqrt(length(dfcorr$r))
UCI<- meanR+SEMR*1.96
LCI<- meanR-SEMR*1.96
mean(filter(dfcorr, dfcorr$location=="I")$r)
mean(filter(dfcorr, dfcorr$location=="O")$r)
baysian_corrGLMM <- brm(r.t ~ location * species + (1|pop), data=dfcorr, family = weibull(link="log"), control = list(adapt_delta = 0.9))
baysian_corrGLMM2 <- brm(r.t ~ location + species + (1|pop), data=dfcorr, family = weibull(link="log"), control = list(adapt_delta = 0.9))
baysian_corrGLMM3 <- brm(r.t ~ location + (1|pop), data=dfcorr, family = weibull(link="log"), control = list(adapt_delta = 0.9))
baysian_corrGLMM_NULL <- brm(r.t ~ 1 + (1|pop), data=dfcorr, family = weibull(link="log"), control = list(adapt_delta = 0.9))
waic.BCG_1<-waic(baysian_corrGLMM)
waic.BCG_2<-waic(baysian_corrGLMM2)
waic.BCG_3<-waic(baysian_corrGLMM3)
waic.BCG_NULL<-waic(baysian_corrGLMM_NULL)
compare(waic.BCG_1,waic.BCG_2) #positive means second is better
compare(waic.BCG_2,waic.BCG_3) #negative means first is better
compare(waic.BCG_2,waic.BCG_NULL) #negative means first is better
summary(baysian_corrGLMM2)
bayes_R2(baysian_corrGLMM2)
ggplot(dfcorr, aes(y=r,x=location))+geom_boxplot()+theme_simple()
ggplot(dfcorr, aes(y=r,x=species))+geom_boxplot()+theme_simple()Totals data
# model
GLMMmyc_lesion <- glmer(binlesion ~ None.Myc * species + (1 | pop) , data = ndatas,family = binomial(link = "logit"))
summary(GLMMmyc_lesion)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: binlesion ~ None.Myc * species + (1 | pop)
## Data: ndatas
##
## AIC BIC logLik deviance df.resid
## 5388.9 5433.4 -2681.5 5362.9 213
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.9159 -3.2800 -0.7426 2.8805 11.6817
##
## Random effects:
## Groups Name Variance Std.Dev.
## pop (Intercept) 0.07038 0.2653
## Number of obs: 226, groups: pop, 11
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.750276 0.090719 -8.270 < 2e-16 ***
## None.Myc -0.017781 0.038118 -0.466 0.640866
## speciesCL 0.415585 0.056183 7.397 1.39e-13 ***
## speciesGA 0.444280 0.053486 8.306 < 2e-16 ***
## speciesGR 0.266576 0.073678 3.618 0.000297 ***
## speciesMR 0.146355 0.057804 2.532 0.011344 *
## speciesSC 0.007849 0.051574 0.152 0.879040
## None.Myc:speciesCL 0.156587 0.048414 3.234 0.001219 **
## None.Myc:speciesGA 0.191932 0.050731 3.783 0.000155 ***
## None.Myc:speciesGR 0.338206 0.069696 4.853 1.22e-06 ***
## None.Myc:speciesMR 0.063131 0.053541 1.179 0.238360
## None.Myc:speciesSC 0.210590 0.051242 4.110 3.96e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) Nn.Myc spcsCL spcsGA spcsGR spcsMR spcsSC N.M:CL N.M:GA
## None.Myc -0.134
## speciesCL -0.369 0.213
## speciesGA -0.385 0.223 0.649
## speciesGR -0.279 0.160 0.466 0.500
## speciesMR -0.340 0.207 0.572 0.614 0.438
## speciesSC -0.381 0.233 0.627 0.660 0.477 0.588
## Nn.Myc:spCL 0.098 -0.786 -0.235 -0.155 -0.110 -0.155 -0.171
## Nn.Myc:spGA 0.094 -0.750 -0.141 -0.235 -0.116 -0.146 -0.169 0.593
## Nn.Myc:spGR 0.086 -0.551 -0.142 -0.151 -0.111 -0.128 -0.145 0.431 0.406
## Nn.Myc:spMR 0.090 -0.711 -0.144 -0.148 -0.092 -0.111 -0.159 0.560 0.534
## Nn.Myc:spSC 0.116 -0.750 -0.191 -0.195 -0.145 -0.169 -0.045 0.589 0.555
## N.M:GR N.M:MR
## None.Myc
## speciesCL
## speciesGA
## speciesGR
## speciesMR
## speciesSC
## Nn.Myc:spCL
## Nn.Myc:spGA
## Nn.Myc:spGR
## Nn.Myc:spMR 0.394
## Nn.Myc:spSC 0.429 0.527options(na.action="na.fail")
dredge(GLMMmyc_lesion)## Fixed term is "(Intercept)"r.squaredGLMM(GLMMmyc_lesion)## The result is correct only if all data used by the model has not changed since model was fitted.## R2m R2c
## 0.02739802 0.04008648# will need to change this ASAP
ggplot(data = ndata,aes(x = 1-None.Myc, y = 100-None.Path))+
stat_summary(fun.y=mean, geom="point")+
geom_smooth(method = "lm")+
geom_point()+
theme_simple()+
facet_wrap("species")+
labs(x = "Mycorrhizal colonization", y="Lesions")
Hypothesis 2: Mycorrhiza & Lesion ~ invasion
Does location impact the effect of myc on lesion?
GLMMmyc_lesion_loc <- glmer(binlesion ~ None.Myc * location * species + (1 | pop), data = ndatas, family = binomial(link = "logit"))
summary(GLMMmyc_lesion_loc)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: binlesion ~ None.Myc * location * species + (1 | pop)
## Data: ndatas
##
## AIC BIC logLik deviance df.resid
## 5185.5 5271.0 -2567.7 5135.5 201
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.6366 -3.2043 -0.3462 2.6760 13.6450
##
## Random effects:
## Groups Name Variance Std.Dev.
## pop (Intercept) 0.0698 0.2642
## Number of obs: 226, groups: pop, 11
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.725383 0.100890 -7.190 6.49e-13 ***
## None.Myc -0.062764 0.054987 -1.141 0.253688
## locationO -0.068081 0.081316 -0.837 0.402458
## speciesCL 0.200476 0.081638 2.456 0.014063 *
## speciesGA 0.296660 0.077883 3.809 0.000139 ***
## speciesGR -1.181296 0.193649 -6.100 1.06e-09 ***
## speciesMR 0.277361 0.084158 3.296 0.000982 ***
## speciesSC -0.021562 0.073106 -0.295 0.768042
## None.Myc:locationO 0.093031 0.080266 1.159 0.246440
## None.Myc:speciesCL 0.324299 0.071788 4.517 6.26e-06 ***
## None.Myc:speciesGA 0.189403 0.072737 2.604 0.009216 **
## None.Myc:speciesGR -0.300771 0.187873 -1.601 0.109393
## None.Myc:speciesMR 0.255496 0.077895 3.280 0.001038 **
## None.Myc:speciesSC 0.101743 0.070113 1.451 0.146743
## locationO:speciesCL 0.398803 0.106396 3.748 0.000178 ***
## locationO:speciesGA 0.301929 0.101835 2.965 0.003028 **
## locationO:speciesGR 1.889287 0.212942 8.872 < 2e-16 ***
## locationO:speciesMR -0.260917 0.111010 -2.350 0.018754 *
## locationO:speciesSC 0.143608 0.103149 1.392 0.163850
## None.Myc:locationO:speciesCL -0.282839 0.100392 -2.817 0.004842 **
## None.Myc:locationO:speciesGA -0.003347 0.105512 -0.032 0.974693
## None.Myc:locationO:speciesGR 0.463051 0.207868 2.228 0.025906 *
## None.Myc:locationO:speciesMR -0.384191 0.109499 -3.509 0.000450 ***
## None.Myc:locationO:speciesSC 0.233745 0.102953 2.270 0.023183 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Correlation matrix not shown by default, as p = 24 > 12.
## Use print(x, correlation=TRUE) or
## vcov(x) if you need itemm<-emmeans(GLMMmyc_lesion_loc, list(~None.Myc| species | location, ~None.Myc| location), type = "response" )## NOTE: Results may be misleading due to involvement in interactionssummary(emm)## $`emmeans of None.Myc, location | species`
## species = AH:
## None.Myc location prob SE df asymp.LCL asymp.UCL
## 1.058488e-16 I 0.3262087 0.02217532 NA 0.28432176 0.3710671
## 1.058488e-16 O 0.3114255 0.02097601 NA 0.27186461 0.3539447
##
## species = CL:
## None.Myc location prob SE df asymp.LCL asymp.UCL
## 1.058488e-16 I 0.3717055 0.02222786 NA 0.32927810 0.4162074
## 1.058488e-16 O 0.4516058 0.02288001 NA 0.40727139 0.4967219
##
## species = GA:
## None.Myc location prob SE df asymp.LCL asymp.UCL
## 1.058488e-16 I 0.3944313 0.02175155 NA 0.35269620 0.4377651
## 1.058488e-16 O 0.4514349 0.02239380 NA 0.40803107 0.4955905
##
## species = GR:
## None.Myc location prob SE df asymp.LCL asymp.UCL
## 1.058488e-16 I 0.1293544 0.02255808 NA 0.09118441 0.1803321
## 1.058488e-16 O 0.4786449 0.02657122 NA 0.42698389 0.5307668
##
## species = MR:
## None.Myc location prob SE df asymp.LCL asymp.UCL
## 1.058488e-16 I 0.3898311 0.02331380 NA 0.34521822 0.4363672
## 1.058488e-16 O 0.3149625 0.02075782 NA 0.27576180 0.3569890
##
## species = SC:
## None.Myc location prob SE df asymp.LCL asymp.UCL
## 1.058488e-16 I 0.3214874 0.01942629 NA 0.28465376 0.3606841
## 1.058488e-16 O 0.3381795 0.02091737 NA 0.29847025 0.3803078
##
## Confidence level used: 0.95
## Intervals are back-transformed from the logit scale
##
## $`emmeans of None.Myc | location`
## location = I:
## None.Myc prob SE df asymp.LCL asymp.UCL
## 1.058488e-16 0.3107155 0.01873775 NA 0.2752289 0.3485770
##
## location = O:
## None.Myc prob SE df asymp.LCL asymp.UCL
## 1.058488e-16 0.3887098 0.01966447 NA 0.3509329 0.4278726
##
## Results are averaged over the levels of: species
## Confidence level used: 0.95
## Intervals are back-transformed from the logit scaleggplot(data = ndata,aes(x = 1-None.Myc, y = 100-None.Path))+
geom_smooth(method = "lm")+
geom_point(aes(color=location))+
theme_simple()+
facet_wrap("species")+
labs(x = "Mycorrhizal colonization", y="Lesions")
pca <- prcomp(ndata[,c(5,9)])
location <- ndata[,13]
g <- ggbiplot(pca, obs.scale = 1, var.scale = 1,
groups = location, ellipse = TRUE,
circle = TRUE)
g <- g + scale_color_discrete(name = '')
g <- g + theme(legend.direction = 'horizontal',
legend.position = 'top')
print(g)
Does location impact lesion alone?
glmerLESION_disp <- glmer (binlesion ~ location * species + (1|pop) + (1|indiv), data = ndatas, family = binomial(link="logit"))## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control
## $checkConv, : Model failed to converge with max|grad| = 0.00135513 (tol =
## 0.001, component 1)summary(glmerLESION_disp)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: binlesion ~ location * species + (1 | pop) + (1 | indiv)
## Data: ndatas
##
## AIC BIC logLik deviance df.resid
## 2011.7 2059.6 -991.8 1983.7 212
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.53231 -0.13210 -0.00971 0.11216 1.14859
##
## Random effects:
## Groups Name Variance Std.Dev.
## indiv (Intercept) 1.11959 1.0581
## pop (Intercept) 0.06426 0.2535
## Number of obs: 226, groups: indiv, 226; pop, 11
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.85482 0.30710 -2.784 0.00538 **
## locationO -0.10392 0.39475 -0.263 0.79235
## speciesCL 0.26989 0.39300 0.687 0.49225
## speciesGA 0.38852 0.37584 1.034 0.30127
## speciesGR -0.88023 0.62967 -1.398 0.16214
## speciesMR 0.38516 0.41882 0.920 0.35776
## speciesSC -0.09661 0.35549 -0.272 0.78581
## locationO:speciesCL 0.45477 0.52759 0.862 0.38870
## locationO:speciesGA 0.47505 0.50259 0.945 0.34456
## locationO:speciesGR 1.77188 0.77503 2.286 0.02224 *
## locationO:speciesMR -0.28686 0.55694 -0.515 0.60651
## locationO:speciesSC -0.02068 0.48262 -0.043 0.96582
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) loctnO spcsCL spcsGA spcsGR spcsMR spcsSC lcO:CL lcO:GA
## locationO -0.703
## speciesCL -0.741 0.551
## speciesGA -0.778 0.579 0.616
## speciesGR -0.455 0.347 0.354 0.376
## speciesMR -0.682 0.522 0.539 0.570 0.340
## speciesSC -0.807 0.608 0.637 0.669 0.393 0.588
## lctnO:spcCL 0.524 -0.747 -0.716 -0.431 -0.253 -0.390 -0.453
## lctnO:spcGA 0.566 -0.787 -0.446 -0.727 -0.272 -0.411 -0.488 0.587
## lctnO:spcGR 0.354 -0.513 -0.273 -0.288 -0.807 -0.269 -0.307 0.378 0.400
## lctnO:spcMR 0.502 -0.709 -0.396 -0.411 -0.250 -0.732 -0.434 0.530 0.558
## lctnO:spcSC 0.575 -0.818 -0.450 -0.473 -0.283 -0.428 -0.721 0.612 0.643
## lcO:GR lcO:MR
## locationO
## speciesCL
## speciesGA
## speciesGR
## speciesMR
## speciesSC
## lctnO:spcCL
## lctnO:spcGA
## lctnO:spcGR
## lctnO:spcMR 0.366
## lctnO:spcSC 0.419 0.580
## convergence code: 0
## Model failed to converge with max|grad| = 0.00135513 (tol = 0.001, component 1)options(na.action="na.fail")
dredge(glmerLESION_disp)## Fixed term is "(Intercept)"## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control
## $checkConv, : Model failed to converge with max|grad| = 0.00135513 (tol =
## 0.001, component 1)r.squaredGLMM(glmerLESION_disp)## R2m R2c
## 0.03076813 0.04469034ggplot(aes(x = location, y = 100-None.Path, color=location), data=ndata)+
geom_boxplot()+
geom_jitter(width=0.1)+
facet_wrap("species")+
theme_simple()
Does location impact mycorrhiza alone?
glmerMYC_disp <- glmer (binmycorr ~ location * species + (1|pop) + (1|indiv), data = ndata, family = binomial(link="logit"))
summary(glmerMYC_disp)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: binmycorr ~ location * species + (1 | pop) + (1 | indiv)
## Data: ndata
##
## AIC BIC logLik deviance df.resid
## 2073.3 2121.2 -1022.7 2045.3 212
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.35863 -0.12130 0.01523 0.09795 1.40036
##
## Random effects:
## Groups Name Variance Std.Dev.
## indiv (Intercept) 2.062e+00 1.4361234
## pop (Intercept) 1.044e-08 0.0001022
## Number of obs: 226, groups: indiv, 226; pop, 11
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.121220 0.390387 0.310 0.7562
## locationO -0.008745 0.526879 -0.017 0.9868
## speciesCL -0.200766 0.515746 -0.389 0.6971
## speciesGA -0.375379 0.491194 -0.764 0.4447
## speciesGR -1.324367 0.829848 -1.596 0.1105
## speciesMR -0.505583 0.551771 -0.916 0.3595
## speciesSC -0.954255 0.471189 -2.025 0.0428 *
## locationO:speciesCL 0.053276 0.706272 0.075 0.9399
## locationO:speciesGA 0.233201 0.669292 0.348 0.7275
## locationO:speciesGR 0.990565 1.025133 0.966 0.3339
## locationO:speciesMR -0.245112 0.745205 -0.329 0.7422
## locationO:speciesSC -0.457001 0.645298 -0.708 0.4788
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) loctnO spcsCL spcsGA spcsGR spcsMR spcsSC lcO:CL lcO:GA
## locationO -0.741
## speciesCL -0.757 0.561
## speciesGA -0.795 0.589 0.602
## speciesGR -0.470 0.349 0.356 0.374
## speciesMR -0.708 0.524 0.536 0.562 0.333
## speciesSC -0.829 0.614 0.627 0.659 0.390 0.586
## lctnO:spcCL 0.553 -0.746 -0.730 -0.439 -0.260 -0.391 -0.458
## lctnO:spcGA 0.583 -0.787 -0.442 -0.734 -0.274 -0.413 -0.483 0.587
## lctnO:spcGR 0.381 -0.514 -0.288 -0.303 -0.809 -0.269 -0.316 0.383 0.405
## lctnO:spcMR 0.524 -0.707 -0.396 -0.416 -0.246 -0.740 -0.434 0.527 0.557
## lctnO:spcSC 0.605 -0.816 -0.458 -0.481 -0.285 -0.428 -0.730 0.609 0.643
## lcO:GR lcO:MR
## locationO
## speciesCL
## speciesGA
## speciesGR
## speciesMR
## speciesSC
## lctnO:spcCL
## lctnO:spcGA
## lctnO:spcGR
## lctnO:spcMR 0.363
## lctnO:spcSC 0.420 0.577options(na.action="na.fail")
dredge(glmerMYC_disp)## Fixed term is "(Intercept)"## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control
## $checkConv, : Model failed to converge with max|grad| = 0.0029301 (tol =
## 0.001, component 1)r.squaredGLMM(glmerMYC_disp)## R2m R2c
## 0.0410656 0.0410656ggplot(aes(x = location, y = 100-None.Myc, color=location), data=ndata)+
geom_boxplot()+
geom_jitter(width=0.1)+
facet_wrap("species")+
theme_simple()
Hypothesis 3 + 4: Lesion ~ Mycorriza * invasion
ggplot(data = ndata,aes(x = 1-None.Myc, y = 100-None.Path, color=location))+
geom_smooth(method = "lm")+
geom_point()+
theme_simple()+
facet_wrap("species")+
labs(x = "Mycorrhizal colonization", y="Lesions")
ggplot(data = ndata,aes(x = 1-None.Myc, y = 100-None.Path, color=location))+
geom_smooth(method = "lm")+
geom_point()+
theme_simple()+
labs(x = "Mycorrhizal colonization", y="Lesions")